Question

Volume of a cone is 1232 cm³ and its height is 24 cm. Find the surface area of the cone. `( π = 22/7)`

Answer 1

Let the radius of the base and slant height of the cone be r cm and lcm, respectively.

Height of the cone, h = 24 cm

Volume of the cone = 1232 cm³

∴ `1/3`πr²h = 1232 cm³

∴ `1232 = 1/3 × 22/7 × r^2 × 24`

⇒ `(1232xx3xx7)/(22xx24) =  r^2    ...("Multiplying both sides by"  3xx7/22xx1/24)`

⇒ r² = 49

⇒ r = `sqrt(49)`

 ⇒ r = 7 cm

Now,

l² = r² + h²

⇒ l² = (7)² + (24)²

⇒ l² = 49 + 576

⇒ l² = 625

⇒ l = `sqrt 625`

⇒ l = 25 cm 

∴ Curved Surface area of the cone = πrl

= `22/7 xx 7 xx 25`

= 550 cm² 

Thus, the surface area of the cone is approximately 550 cm².