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

(i) length = 22 cm, breadth = 12 cm and height = 7.5 cm

(ii) length = 15 m, breadth = 6 m and height = 9 dm

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

(iv) length = 48 cm, breadth = 6 dm and height = 1 m

The dimensions of a rectangular water tank are 2 m 75 cm by 1 m 80 cm by 1 m 40 cm. How many litres of water does it hold when filled to the brim?

A solid rectangular piece of iron measures 1.05 m x 70 cm x 1.5 cm. Find the weight of this piece in kilograms if 1 cm³ of iron weighs 8 grams.

The area of a courtyard is 3750 m². Find the cost of covering it with gravel to a height of 1 cm if the gravel costs Rs. 6.40 per cubic metre.

How many persons can be accommodated in a hall of length 16 m, breadth 12.5 m and height 4.5 m, assuming that 3.6 m³ of air is required for each person?

A cardboard box is 1.2 m long, 72 cm wide and 54 cm high. How many bars of soap can be put into it if each bar measures 6 cm x 4.5 cm x 4 cm?

The size of a matchbox is 4 cm x 2.5 cm x 1.5 cm. What is the volume of a packet containing 144 matchboxes? How many such packets can be placed in a carton of size 1.5 m x 84 cm x 60 cm?

How many planks of size 2 m x 25 cm x 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, assuming that there is no wastage?

How many bricks, each of size 25 cm x 13.5 cm x 6 cm, will be required to build a wall 8 m long, 5.4 m high and 33 cm thick?

A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring 22 cm x 12.5 cm x 7.5 cm. If of the total volume of the wall consists of mortar, how many 12bricks are there in the wall?

Hint. Volume of bricks in the wall = {(1500 x 30 x 400) x (1500 x 30 x 400)1 cm³.

Find the capacity of a rectangular cistern in litres whose dimensions are 11.2 m x 6 m x 5.8 m. Find the area of the iron sheet required to make the cistern.

The volume of a block of gold is 0.5 m³. If it is hammered into a sheet to cover an area of 1 hectare, find the thickness of the sheet.

The rainfall recorded on a certain day was 5 cm. Find the volume of water that fell on a 2-hectare field.

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

A pit 5 m long and 3.5 m wide is dug to a certain depth. If the volume of earth taken out of it is 14 m³, what is the depth of the pit?

A rectangular water tank is 90 cm wide and 40 cm deep. If it can contain 576 litres of water, what is its length?

A beam of wood is 5 m long and 36 cm thick. It is made of 1.35 m³ of wood. What is the width of the beam?

The volume of a room is 378 m³ and the area of its floor is 84 m². Find the height of the room.

A swimming pool is 260 m long and 140 m wide. If 54600 cubic metres of water is pumped into it, find the height of the water level in it.

Find the volume of wood used to make a closed box of outer dimensions 60 cm x 45 cm x 32 cm, the thickness of wood being 2.5 cm all around.

Find the volume of iron required to make an open box whose external dimensions are 36 cm x 25 cm x 16.5 cm, the box being 1.5 cm thick throughout. If 1 cm³ of iron weighs 8.5 grams, find the weight of the empty box in kilograms.

A box with a lid is made of wood which is 3 cm thick. Its external length, breadth and height are 56 cm, 39 cm and 30 cm respectively. Find the capacity of the box. Also find the volume of wood used to make the box.

The external dimensions of a closed wooden box are 62 cm, 30 cm and 18 cm. If the box is made of 2-cm-thick wood, find the capacity of the box.

A closed wooden box 80 cm long, 65 cm wide and 45 cm high, is made of 2.5-cm-thick wood. Find the capacity of the box and its weight if 100 cm³ of wood weighs 8 g.

Find the volume, lateral surface area and the total surface area of a cube each of whose edges measures:

(i) 7 m (ii) 5.6 cm (iii) 8 dm 5 cm

The surface area of a cube is 1176 cm². Find its volume.

The volume of a cube is 729 cm³. Find its surface area.

The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recast into cubes, each of side 45 cm. How many cubes are formed?

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

A solid cubical block of fine wood costs 256 at 500 per m³. Find its volume and the length of each side.

Find the volume, curved surface area and total surface area of each of the cylinders whose dimensions are:

(i) radius of the base = 7 cm and height = 50 cm

(ii) radius of the base = 5.6 m and height = 1.25 m

(iii) radius of the base = 14 dm and height = 15 m

A milk tank is in the form of a cylinder whose radius is 1.5 m and height is 10.5 m. Find the quantity of milk in litres that can be stored in the tank.

A wooden cylindrical pole is 7 m high and its base radius is 10 cm. Find its weight if the wood weighs 225 kg per cubic metre.

Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?

The volume of a circular iron rod of length 1 m is 3850 cm³. Find its diameter.

A closed cylindrical tank of diameter 14 m and height 5 m is made from a sheet of metal. How much sheet of metal will be required?

The circumference of the base of a cylinder is 88 cm and its height is 60 cm. Find the volume of the cylinder and its curved surface area.

The lateral surface area of a cylinder of length 14 m is 220 m². Find the volume of the cylinder.

The volume of a cylinder of height 8 cm is 1232 cm³. Find its curved surface area and the total surface area.

The radius and height of a cylinder are in the ratio 7 : 2. If the volume of the cylinder is 8316 cm 3, find the total surface area of the cylinder.

The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm. Find the volume of the cylinder.

A particular brand of talcum powder is available in two packs, a plastic can with a square base of side 5 cm and of height 14 cm, or one with a circular base of radius 3.5 cm and of height 12 cm. Which of them has greater capacity and by how much?

Find the cost of painting 15 cylindrical pillars of a building at Rs. 2.50 per square metre if the diameter and height of each pillar are 48 cm and 7 metres respectively.

A rectangular vessel 22 cm by 16 cm by 14 cm is full of water. If the total water is poured into an empty cylindrical vessel of radius 8 cm, find the height of water in the cylindrical vessel.

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?

A solid cube of metal each of whose sides measures 2.2 cm is melted to form a cylindrical wire of radius 1 mm. Find the length of the wire so obtained.

How many cubic metres of earth must be dug out to sink a well which is 20 m deep and has a diameter of 7 metres? If the earth so dug out is spread over a rectangular plot 28 m by 11 m, what is the height of the platform so formed?

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Hint. Required height =

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of the road roller is 84 cm and its length is 1 m.

A cylinder is open at both ends and is made of 1.5-cm-thick metal. Its external diameter is 12 cm and height is 84 cm. What is the volume of metal used in making the cylinder? Also, find the weight of the cylinder if 1 cm ' of the metal weighs 7.5 g.

Hint. External radius = 6 cm, internal radius = 4.5 cm.

Volume of metal =

.

The length of a metallic tube is 1 metre, its thickness is 1 cm and its inner diameter is 12 cm. Find the weight of the tube if the density of the metal is 7.7 grams per cubic centimetre.

Hint. Weight of 1 cm³ of metal = 7.7 g.

Its volume =

The maximum length of a pencil that can be kept in a rectangular box of dimensions

12 cm x 9 cm x 8 cm, is

The total surface area of a cube is 150 cm². Its volume is

The volume of a cube is 343 cm³. Its total surface area is

The cost of painting the whole surface area of a cube at the rate of is 10 paise per cm²Rs. 264.60. Then, the volume of the cube is

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall 8 m long, 6 m high and 22.5 cm thick?

How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?

The edges of a cuboid are in the ratio 1: 2: 3 and its surface area is 88 cm2. The volume of the cuboid is

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

The surface area of a (10 cm x 4 cm x 3 cm) brick is

An iron beam is 9 m long, 40 cm wide and 20 cm high. If 1 cubic metre of iron weighs 50 kg, what is the weight of the beam?

A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and its breadth is 3.5 m, the depth of the reservoir is

The dimensions of a room are (10 mx8mx 3.3 m). How many men can be accommodated in this room if each man requires 3 m³ of space?

A rectangular water tank is 3 m long, 2 m wide and 5 m high. How many litres of water can it hold?

The area of the cardboard needed to make a box of size 25 cm x 15 cm x 8 cm will be

The diagonal of a cube measures cm. Its volume is

The diagonal of a cube is cm long. Its total surface area is

If each side of a cube is doubled then its volume

If each side of a cube is doubled, its surface area

Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is

Five equal cubes, each of edge 5 cm, are placed adjacent to each other. The volume of the cuboid so formed, is

A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?

If the capacity of a cylindrical tank is 1848 m³ and the diameter of its base is 14 m, the depth of the tank is

The ratio of the total surface area to the lateral surface area of 20 cm and height 60 cm, is

The number of coins, each of radius 0.75 cm and thickness 0.2 rightcm, to be melted to make aright circular cylinder of height 8 cm and base radius 3 cm is

66 cm³ of silver is drawn into a wire 1 mm in diameter. The length of the wire will be

The height of a cylinder is 14 cm and its diameter is 10 cm. The volume of the cylinder is

The height of a cylinder is 80 cm and the diameter of its base is 7 cm. The whole surface area of the cylinder is

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

The diameter of a cylinder is 14 cm and its curved surface area is 220 cm². the volume of the cylinder is

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

Find the volume of a cube whose total surface area is 384 cm².

How many soap cakes each measuring 7 cm 7cmx 5 cm x 2.5 cm can be placed in a box of size 56cm x 40 cm x 25 cm?

The radius and height of the cylinder are in the ratio 5 : 7 and its volume is 550 cm³. Find its radius and height.

Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder with a height of 10 cm and a diameter of 4.5 cm.

Find the surface area of a chalk box, whose length, breadth and height are 18 cm, 10 cm and 8 cm respectively.

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

The circumference of the circular base of a cylinder is 44 cm and its height is 15 cm. The volume of the cylinder is

The area of the base of a circular cylinder is 35 cm² and its height is 8 cm. The volume of the cylinder is

A cuboid having dimensions 16 m x 11 m x 8 m is melted to form a cylinder of radius 4 m. What is the height of the cylinder?

The dimensions of a cuboid are 8m x 6 m x4 m. Its lateral surface area is

The length, breadth and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm³. The whole surface area of the cuboid is

The surface area of a cube is 384 cm². Its volume is

Fill in the blanks:

(i) If l, b, h be the length, breadth and height of a cuboid, then its whole surface area = (………… ) sq units.

(ii) If l, b, h be the length, breadth and height of a cuboid, then its lateral surface area = (…………… ) sq units.

(iii) If each side of a cube is a, then its lateral surface area is………..sq units.

(iv) If r is the radius of the base and h be the height of a cylinder, then its volume is (………….. ) cubic units.

(v) If r is the radius of the base and h be the height of a cylinder, then its lateral surface area is (…………. ) sq units.