The radii of two solid spheres are 10 cm and 20 cm. The ratio between their volumes is :

1. 3 : 8

2. 1 : 4

3. 1 : 8

4. 8 : 3

A cone and a sphere have equal volumes. If height of the cone = radius of the sphere = 10 cm, the radius of the cone is :

1. 40 cm

2. 10 cm

3. 30 cm

4. 20 cm

By applying force on an uniform metallic wire, the wire is extended four times along its length with same width all around. Then :

(i) The volume of metal in both the cases is same.

(ii) The surface area of solid wires in both the cases is same.

Which of the above statements is/are true?

1. only (i)

2. only (ii)

3. both (i) and (ii)

4. neither (i) nor (ii)

The given figure shows a toy made of very thin metal sheet. The toy has the hemisphere, a cylinder and a cone all of the same radius.

Assertion(A): The minimum area of metal sheet required is:

Curved surface area of conical part + curved surface area of cylinder part - curved surface area of hemispherical part

Reason(R): Metal sheet required = curved surface area of (conical part + cylindrical part + hemispherical part)

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.