If the radius if a sphere is 2r, then its volume will be

The total surface area of a cube is 96 cm^{2}. The volume of the cube 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

In a cylinder, radius is doubled and height is halved, then curved surface area will be

The total surface area of a cone whose radius is r/2 and slant height 2L is

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

The lateral surface area of a cube is 256 m^{2}_{.}The volume of the cube is

The number of planks of dimensions (4m x 50cm x 20cm) that can be stored in a pit which is 16 m long, 12 m wide and 40 m deep is

The length of the longest pole that can be put in a room of dimensions (10 m x 10m x 5m) is

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

Write whether True or False and justify your answer

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

If the radius of a right circular cone is halved and height is doubled, then volume will remain unchanged.

In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

The volume of the Largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere radius r.

A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.

If the Length of the diagonal of a cube is 6√3 cm, then the Length of the edge of the cube is 3 cm.

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 6 : π.

If the radius of a cylinder is doubled and height is halved, the volume will be doubled.

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [use π = 3.14]

A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m^{3}. If the present depth of water is 1.3 m, then find the volume of water already used from the tank.

Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?

Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, find how many litres of milk is needed to serve 1600 students.

A cylindrical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 m^{2}. How many revolutions did it make?

A small village, having a population of 5000, requires 75 L of water per head per day. The village has got an overhead tank of measurement 40 m x 25 m x 15 m. For how many days will the water of this tank last?

A shopkeeper has one spherical laddoo of radius 5 cm. With the same amount of material, how many laddoos of radius 2.5 cm can be made?

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface of the solid so formed.

A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimetres of iron has been used in making the tube?

A semi-circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.

A cloth having an area of 165 m^{2} is shaped into the form of a conical tent of radius 5m.

(i) How many students can sit in the tent, if a student on an average occupies 5/7 m^{2} on the ground?

(ii) Find the volume of the cone.

The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kL of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.

A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.

A sphere and a right circular cylinder of the same volumes. By what percentage does the diameter of the height?

30 circular plates, each of radius 14 cm and thickness 3 cm are placed one above the another to form a cylindrical solid. Find

(i) the total surface area.

(ii) volume of the cylinder so formed.