Question

A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:

A. 1000 times

B. 100 times

C. 10 times

D. No Change

E. None of the above

Correct Answer : 10 times. Choice C

Explanatory Answer

Let the radius of the small spheres be ‘r’ cm.

The amount of metal remains the same in both cases.

Hence, volume of the spherical metal of radius 10 cm should be equal to the volume of the 1000 smaller spheres of radius ‘r’ cm put together.

Therefore, r = 1 cm.

Surface area of a spherical metal of radius 10 cm is

Surface area of 1000 smaller spheres put together is

Thus the surface area increased by 10 times.

A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:

A. 1000 times

B. 100 times

C. 10 times

D. No Change

E. None of the above

Correct Answer : 10 times. Choice C

Explanatory Answer

Let the radius of the small spheres be ‘r’ cm.

The amount of metal remains the same in both cases.

Hence, volume of the spherical metal of radius 10 cm should be equal to the volume of the 1000 smaller spheres of radius ‘r’ cm put together.

Therefore, r = 1 cm.

Surface area of a spherical metal of radius 10 cm is

Surface area of 1000 smaller spheres put together is

Thus the surface area increased by 10 times.