Question

Find the volume of a cone, if its total surface area is 7128 sq. cm and radius of base is 28 cm. `(π = 22/7)`

Answer 1

Let the perpendicular height and the slant height of the cone be h cm and l cm, respectively.

Radius of the base of cone, r = 28 cm

Total surface area of the cone = 7128 cm²
∴ πr(r + l) = 7128 cm²

⇒ `22/7 xx 28 xx (28 + "l") = 7128`

⇒ `7128 xx 7/22 xx 1/28 = l + 28`

⇒ 81 − 28 = l

⇒ l = 53 cm

Now,

l² = r² + h² 

⇒ (53)² = (28)² + h²

⇒ h² = 2809 − 784 = 2025

⇒ h = `sqrt 2025`

⇒ h = 45 cm

∴ Volume of the cone = `1/3`πr²h

= `1/3 xx 22/7 xx (28)^2 xx 45`

= 36960 cm³

Thus, the volume of the cone is 36960 cm³.