I would like to give a question which i could not solve.

Rd sharma class 10 maths exercise-16.1 mensuration.

In this question we have to find the diameter of the base of the cone having the surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm.

Need help

Given,

The height of the cone = 28 cm

Surface area of the solid metallic sphere = 616 cm3

We know that,

Surface area of the sphere = 4πr2

So, 4πr2 = 616

r2 = 49

r = 7

Radius of the solid metallic sphere = 7 cm

Let’s assume r to be the radius of the cone

We know that,

Volume of the cone = 1/3 πr2h

= 1/3 πr2 (28) ….. (i)

Volume of the sphere = 4/3 πr3

= 4/3 π73 ………. (ii)

On equating equations (i) and (ii), we have

1/3 πr2 (28) = 4/3 π73

Eliminating the common terms, we get

r2 (28) = 4 x 73

r2 = 49

r =7

So, diameter of the cone = 7 x 2 = 14 cm

Therefore, the diameter of the base of the cone is 14 cm