Question

A hollow sphere of external diameter 10 cm and internal diameter 6 cm is melted and made into a solid right circular cone of height 8 cm. Find the radius of the cone so formed.

[Use π = `22/7`]

Answer 1

Given

∴ External diameter of sphere (d₁) = 10 cm

∴ External radius of sphere (r₁) = 5 cm

∵ Internal diameter of sphere (d₂) = 6 cm

∴ Internal radius of sphere (r₂) =3 cm

Height of cone (h) = 8 cm

Let the radius of the cone = r

Now, Volume of sphere = `4/3 π(r_1^3 − r_2^3)`

= `4/3 π(125 − 27)`

= `4/3π × 98`

And Volume of cone = `1/3πhr^2`

According the question,

Volume of sphere = Volume of cone

`4/3π × 98 = (πr^2h)/3`

`4/3 × 98 = r^2 × 8`

`r^2 = (4 × 98)/8`

= 49

r = 7 cm

Hence, the radius of the cone is 7cm.