Question

the surface area of a solid metallic sphere is 616 cmsq . it is melted and recast into a cone of height 28 cm. find the diameter of the base of the cone so formed .

Answer 1

Volume of sphere = volume of cone

Answer 2

Answer:-

Given:-

The height of the cone = 28 cm

Surface area of the solid metallic sphere = 616 cm3

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

Using formula:-

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