Question

Eight spheres of same volumes are recasted by melting a metallic sphere with radius of 10 cm. Find the volume of the recasted sphere.

Answer 1

Given,

Radius of the metallic sphere (r) = 10 cm

∴ Volume of sphere = \(\frac { 4 }{ 3 }\)πr³

= \(\frac { 4 }{ 3 }\) × π × r × (10)³

Let the radius of each recasted spheres be R.

∴ The volume of large sphere =8 × volume of spheres with radius R

Hence, radius of the sphere casted = 5 cm.

Surface area of sphere = 4πR²

= 4 × π × (5)²

=4 × π × 25

= 100π cm²

Hence, surface area of casted sphere = 100π cm²