Question

Curved surface area of a cone is 251.2 cm² and radius of its base is 8 cm. Find its slant height and perpendicular height. (π = 3.14)

Answer 1

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

Radius of the base of cone, r = 8 cm
Curved surface area of the cone = 251.2 cm²

∴ πrl = 251.2 cm²

⇒ 3.14 x 8 x l = 251.2

⇒ l = `251.2/25.12` = 10 cm

Now,

r² + h² = l²

⇒ (8)² + h² = (10)²

⇒ 64 + h² = 100 

⇒ h² = 100 - 64 = 36

⇒ h = `sqrt36` = 6 cm

Thus, the slant height and perpendicular height of the cone are 10 cm and 6 cm, respectively.