Find the volume, the lateral surface area and the total surface area of the cuboid whose dimensions are:

(i) length = 12 cm, breadth = 8 cm and height = 4.5 cm

(ii) length = 26 m, breadth = 14 m and height = 6.5 m

(iii) length = 15 m, breadth = 6 m and height = 5 dm

(iv) length = 24 m, breadth = 25 cm and height = 6 m

Find the capacity of a closed rectangular cistern whose length is 8 m, breadth 6 m and depth 2.5 m. Also, find the area of the iron sheet required to make the cistern.

The dimensions of a room are It has one door of dimensions and two windows, each of dimensions Find the cost of white washing the walls at Rs. 6.40 per square metre.

How many planks of dimensions (5m × 25cm × 10cm) can be stored in a pit which is 20 m long, 6 m wide and 80 cm deep?

How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick if each brick measures (25 cm × 11.25 cm × 6 cm)?

A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring Ifof the total volume of the wall consists of mortar, how many bricks are there in the wall?

An open rectangular cistern when measured from outside is 1.35 m long, 1.08 m broad and 90 cm deep. It is made up of iron, which is 2.5 cm thick. Find the capacity of the cistern and the volume of the iron used.

A river 2 m deep and 45 m wide is flowing at the rate of 3 km per hour. Find the volume of water that runs into the sea per minute.

A box made of sheet metal costs Rs 1620 at Rs 30 per square metre. If the box is 5 m long and 3 m wide, find its height.

Find the length of the longest pole that can be put in a room of dimensions

How many person can be accommodated in a dining hall of dimensions assuming that each person requires 5 cubic metres of air?

A classroom is 10 m long, 6.4 m wide and 5 m high. If each student be given of the floor area, how many students can be accommodated in the room? How many cubic metres of air would each student get?

The volume of a cuboid is Its length is 16 m, and its breadth and height are in the ratio 3:2. Find the breadth and height of the cuboid.

The surface area of a cuboid is Its length and breadth are 14 cm and 11 cm respectively. Find its height.

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures (a) 9m, (b) 6.5 cm. [Take ]

The total surface area of a cube is Find its volume.

The lateral surface area of a cube is Find its volume.

The volume of a cube is Find its surface area.

Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the lateral surface area of the new cube formed.

In a shower, 5 cm of rain falls. Find the volume of water that falls on 2 hectares of ground.

Find the volume and curved surface area of a right circular cylinder of height 21 cm and base radius 5 cm.

The diameter of a cylinder is 28 cm and its height is 40 cm. Find the curved surface area, total surface area and the volume of the cylinder.

Find the weight of a solid cylinder of radius 10.5 cm and height 60 cm if the material of the cylinder weigh 5 g per cm³.

The curved surface area of a cylinder is and its diameter is 20 cm. Find its height and volume.

The curved surface area of a cylinder is and the circumference of its base is 110 cm. Find the height and the volume of the cylinder.

The radius of the base and the height of a cylinder are in the ratio 2:3. If its volume is find the total surface area of the cylinder.

The total surface area of a cylinder is Its curved surface area is one-third of its total surface area. Find the volume of the cylinder.

The total surface area of a solid is and its curved surface area is of the total surface area. Find the volume of the cylinder.

The sum of the height and radius of the base of a solid cylinder is 37 m. If the total surface area of the cylinder be find its volume.

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the volume of the cylinder if its total surface area is

of gold is drawn into a wire 0.1 mm in diameter. Find the length of the wire.

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces.

A powder tin has a square base with side 12 cm and height 17.5 cm. another is cylindrical with diameter of its base 12 cm and height 17.5 cm. Which has more capacity and by how much?

A cylindrical bucket, 28 cm in diameter and 72 cm high, is full of water. The water is emptied into a rectangular tank, 66 cm long and 28 cm wide. Find the height of the water level in the tank.

If of cast iron weighs 21 g, find the weight of a cast iron pipe of length 1 m with a bore of 3 cm in which the thickness of the metal is 1 cm.

A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.

The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up on writing 33o words on an average. How many words would use up a bottle of ink containing one-fifth of a litre?

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite fitted into it. The diameter of the pencil is 7 mm, the diameter of the graphite is 1 mm and the length of the pencil is 10 cm. calculate the weight of the whole pencil, if the specific gravity of the wood is and that of the graphite is

Find the volume, curved surface area and the total surface area of a cone having base radius 35 cm and height 84 cm.

Find the volume, curved surface area and the total surface area of a cone whose height and slant height are 6 cm and
10 cm respectively. (Take )

The volume of a right circular cone is and its height is 12 cm. Find its slant height and its curved surface area.

The circumference of the base of a cone is 44 cm and its slant height is 25 cm. Find the volume and curved surface area of the cone.

A cone of slant height 25 cm has a curved surface area Find the height and volume of the cone.

Find the volume of a cone having radius of the base 35 cm and slant height 37 cm.

The curved surface area of a cone is and its diameter is 70 cm. Find its slant height.

How many metres of cloth, 2.5 m wide, will be required to make a conical tent whose base radius is 7 m and height 24 metres?

A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone having base radius 1.2 cm. Find its height.

Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Show that their volumes are in the ratio 3:1.

A circus tent is cylindrical to a height of 3 meters and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.

A conical tent is to accommodate 11 persons. Each person must have of the space on the ground and of air to breath. Find the height of the cone.

A cylindrical bucket, 32 cm high and 18 cm of radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and the slant height of the heap.

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius and height of each has the ratio 3:4.

An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that of iron weighs 7.5 g

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be of the volume of the given cone, at what height above the base, the section has been made?

From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid.

Water flows at the rate of 10 meters per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the surface 40 cm and depth 24 cm?

Find the volume and surface area of a sphere whose radius is:

(i) 3.5 cm

(ii) 4.2 cm

(iii) 5 m

The volume of a sphere is Find its radius and hence its surface area.

Find the surface area of a sphere whose volume is

The surface area of a sphere is Find its radius and volume.

The surface area of a sphere is Find its volume.

The outer diameter of a spherical shell is 12 cm and its inner diameter is 8 cm. Find the volume of metal contained in the shell. Also, find its outer surface area.

How many lead shots, each 3 mm in diameter, can be made from a cuboid with dimensions

How many lead balls, each of radius 1 cm, can be made from a sphere of radius 8 cm?

A solid sphere of radius 3 cm is melted and then cast into smaller spherical balls, each of diameter 0.6 cm. Find the number of small balls thus obtained.

A metallic sphere of radius 10.5 cm is melted and then recast into smaller cones, each of radius 3.5 cm and height 3 cm. How many cones are obtained?

How many spheres 12 cm in diameter can be made from a metallic cylinder of diameter 8 cm and height 90 cm?

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire.

The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.

A sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm. Find the diameter of the base of the cone.

A spherical cannonball 28 cm in diameter is melted and cast into a right circular cone mould, whose base is 35 cm in diameter. Find the height of the cone.

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.

The radii of two spheres are in the ratio 1:2. Find the ratio of their surface areas.

The surface areas of two spheres are in the ratio 1:4. Find the ratio of their volumes.

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

A cylindrical bucket with base radius 15 cm is filled with water up to a height of 20 cm. A heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water. Find the increase in the level of water.

A hemisphere of lead of radius 9 cm is cast into a right circular cone of height 72 cm. Find the radius of the base of the cone.

A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles are required to empty the bowl?

A hollow spherical shell is made of a metal of density If its internal and external radii are 8 cm and 9 cm respectively, find the weight of the shell.

A hemispherical bowl is made of steel 0.5 cm thick. The inside radius of the bowl is 4 cm. Find the volume of steel used in making the bowl.

The length, breadth and height of a cuboid are 15 cm, 12 cm, and 4.5 cm respectively. Its volume is

A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its total surface area is

The length, breadth and height of a cuboid are 15 m, 6 m and 5 dm respectively. The lateral surface area of the cuboid is

A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is

The length of the longest rod that can be placed in a room of dimensions (10m × 10m × 5m) is

What is the maximum length of a pencil that can be placed in a rectangular box of dimensions (8cm × 6cm × 5cm)?
(Given )

The number of planks of dimensions (4m × 5m × 2m) that can be stored in a pit which is 40, long 12 m wide and 16 m deep, is

How many planks of dimensions (5m × 25cm × 10cm) can be stored in a pit which is 20 m long, 6 m wide and 50 cm deep?

How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick if each brick measures (25cm × 11.25 cm × 6cm)?

How many persons can be accommodated in a dining hall of dimensions (20m × 15m × 4.5m), assuming that each person requires 5m³ of air?

A river 1.5 m deep and 30 m wide is flowing at the rate of 3 km per hour. The volume of water that runs into the sea minute is

The lateral surface area of a cube is 256m². The volume of the cube is

The total surface area of a cube is 96 cm². The volume of the cube is

The volume of a cube is 512 cm³. Its total surface area is

The length of the longest rod that can fit in a cubical vessel of side 10 cm, is

If the length of diagonal of a cube is then its surface area is

If each edge of a cube is increased by 50%, then the percentage increase in its surface area is

Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. The lateral surface area of the new cube formed is

In a shower, 5 cm of rain falls. What is the volume of water that falls on 2 hectares of ground?

Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is

If each side of a cube is doubled, then its volume

The diameter of the base of a cylinder is 6 cm and its height is 14 cm. The volume of the cylinder is

If the diameter of a cylinder is 28 cm and its height is 20 cm, then its curved surface area is

If the curved surface area of a cylinder is 1760 cm² and its base radius is 14 cm, then its height is

The height of a cylinder is 14 cm and its curved surface area is 264 cm². The volume of the cylinder is

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. The height of the pillar is

The radii of two cylinders are in the ratio 2 :3 and their heights are in the ratio 5 :3. The ratio of their curved surface area is

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5:3. The ratio of their volumes is

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is then its total surface area is

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 cm², then the volume of the cylinder is

In a cylinder, if the radius is halved and the height is doubled, then the volume will be

The number of coins 1.5 cm in diameter and 0.2 cm thick to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm is

The radius of a wire is decreased to one-third. If volume remains the same, the length will become

The diameter of a roller, 1 m long, is 84 cm. If it takes 500 complete revolutions to level a playground, the area of the playground is

2.2 dm³ of lead is to be drawn into a cylindrical wire 0.50 cm in diameter. The length of the wire is

The lateral surface area of a cylinder is

The height of a cone is 24 cm and the diameter of its base is 14 cm. The curved surface area of the cone is

The volume of a right circular cone of height 12 cm and base radius 6 cm, is

How much cloth 2.5 m wide will be required to make a conical tent having base radius 7 m and height 24 m?

The volume of a cone is 1570 cm³ and its height is 15 cm. What is the radius of the cone? (Use)

The height of a cone is 21 cm and its slant height is 28 cm. The volume of the cone is

The volume of a right circular cone of height 24 cm is 1232 cm³. Its curved surface area is

If the volumes of two cones be in the ratio 1 : 4. and the radii of their bases be in the ratio 4 : 5, then the ratio of their heights is

If the height of a cone is doubled, then its volume is increased by

The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is

The ratio of the volumes of a right circular cylinder and a right circular cone of the same base and the same height will be

A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is

The radii of the bases of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. Then, their volumes are in the ratio

If the height and the radius of a cone are doubled, the volume of the cone becomes

A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to make solid cones of height 1 cm and base radius 1 mm. The volume of is

A conical tent is to accommodate 11 persons such that each person occupies 4m² of space on the ground. They have 220 m³ of air to breathe. The height of the cone is

The volume of a sphere of radius 2r is

The volume of a sphere of radius 10.5 cm is

The surface area of a sphere of radius 21 cm is

The surface area of a sphere is 1386 cm². Its volume is

If the surface area of a sphere is then its volume is

The volume of a sphere is 38808 cm³. Its surface area is

If the ratio of the volumes of two spheres is 1 : 8, then the ratio of their surface area is

A solid metal ball of radius 8 cm is melted and cast into smaller balls, each of radius 2cm. The number of such balls is

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is

A solid lead ball of radius 6 cm is melted and then drawn into a wire of diameter 0.2 cm. The length of wire is

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones will be

How many lead shots, each 0.3 cm in diameter, can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm ?

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is

A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm. The radius of the base of the cone is

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. The radius of the third ball is

The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface areas of the balloons in two cases is

The volumes of the two spheres are in the ratio 64 : 27 and the sum of their radii is 7 cm. The difference of their total surface areas is

A hemispherical bowl of radius 9 cm contains a liquid. This liquid is to be filled into cylindrical small bottles of diameter 3 cm and height 4 cm. How many bottles will be needed to empty the bowl?

A cone and a hemisphere have equal bases and equal volumes. The ratio of their heights is

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is

If the volume and the surface area of a sphere are numerically the same, then its radius is

Which is false in case of a hollow cylinder?

Which is false?

For a right circular cylinder of base radius = 7 cm and height = 14 cm, which is false?

Which is false?

A metal pipe is 63 cm long. Its inner diameter is 4 cm and the outer diameter is 4.4 cm. Then,

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

A right circular cylinder just encloses a sphere of radius (as shown in the figure). Then, the surface area of the sphere is equal to the curved surface area of the cylinder.

The largest possible right circular cone is cut out of a cube of edge cm. The volume of the cone is

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be

If the length of diagonal of a cube is then the length of each edge of the cube is 3 cm.

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of
5 : 3. Then, the ratio of their volumes is

The total surface area of a cone whose radius is and slant height is

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is

The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is

A copper sphere of diameter 6 cm is melted and drawn into 36 cm long wire of uniform circular cross-section. Then, its radius is

Find the lateral surface area and the total surface area of a cube of side 8 cm.

Find the lateral surface area and the total surface area of a cuboid of dimensions

The total surface area of a cylinder is 462 cm² and its curved surface area is one-third of its total surface area. Find the volume of the cylinder.

The length and breadth of a room are in a ratio 3 : 2. The cost of carpeting the room at Rs 25 per m² is Rs 1350 and the cost of papering the four walls at Rs 15 per m² is Rs 2580. If one door and two windows occupy 8m², find the dimensions of the room.

If the radius of a sphere is increased by 10%, prove that its volume will be increased by 33.1%.

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone.

A rectangular tank measuring 5m × 4.5m × 2.1 m is dug in the centre of the field measuring 13.5m × 2.5 m. The earth dug out is spread over the remaining portion of the field. How much is the level of the field raised?

A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

The volume of a right circular cone is 9856 cm³. If the diameter of its base is
28 cm, find the height of the cone.

Into a circular drum of radius 4.2 m and height 3.5 m, how many full bags of wheat can be emptied if the space required for wheat in each bag is

A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. Find the height of the embankment.

How many metres of cloth 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and whose height is 24 m?

The volume of a solid cylinder is 1584 cm³ and its height is 14 cm. Find its total surface area.

The volume of two spheres are in the ratio 64 : 27. Find the difference of their surface areas if the sum of their radii is 7 cm.

The radius and height of a right circular cone are in the ratio 4 : 3. and its volume is 2156 cm³. Find the curved surface area of the cone.

The radius of the base of a cone is 14 cm and its height is 24 cm. Find the volume, curved surface area and the total surface area of the cone.

Two cylindrical vessels are filled with oil. Their radii are 15 cm and 10 cm respectively and their heights are 25 cm and 18 cm respectively. Find the radius of the cylindrical vessel 33 cm in height which will just contain the oil of the two given vessels.

The ratio of the curved surface area and the total surface area of a circular cylinder is 1:2 and the total surface area is 616 cm². Find its volume.