Question

The surface area of a solid metallic sphere is 616cm2. It is melted and recast into a cone of height 28cm. Find the diameter of the base of the cone so formed.

Answer 1

Hey.

Here is the answer.

As surface area of sphere = 4πr^2=616 cm^2

so, r^2 = 616/4π

so, r = 49.02 cm

So, volume of sphere = 4/3 π r^3

= 4/3 π (49.02)^3

= 493402.28 cm^3

= volume of the cone casted

= 1/3 π R^2 h

= 1/3 π R^2 ×28

So, 493402.28 = 1/3 π R^2 ×28

or, R^2 = 493402.28×3 /28π

or, R = 129.72 cm

So, required radius is 129.72 cm.

Thanks.