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

Given: Radius (r) = 8 cm, curved surface area of cone = 251.2 cm²

To find: Slant height (l) and the perpendicular height (h) of the cone

i.Curved surface area of cone = πrl

∴ 251.2 = 3.14 x 8 x l

\(l=\frac{251.2}{3.14\times 8}\)

\(=\frac{25120}{314\times 8}\)

\(=\frac{3140}{314}\)

∴ l = 10 cm

ii. Now, l² = r² + h²

∴ 10² = 8² + h²

∴ 100 = 64 + h²

∴ 100 – 64 = h²

∴ h² = 36

∴ h = √36 … [Taking square root on both sides]

= 6 cm

∴ The slant height and the perpendicular height of the cone are 10 cm and 6 cm respectively.