Question

Surface area of a cone is 188.4 sq.cm and its slant height is 10 cm. Find its perpendicular height (π = 3.14).

Answer 1

Given: Length (l) =10 cm, curved surface area of the cone = 188.4 sq.cm

To find: Perpendicular height (h) of the cone

i.Curved surface area of the cone = πrl

∴ 188.4 = 3.14 x r x 10

\(r=\frac{188.4}{3.14\times 10}\)

\(=\frac{1884}{314}\)

r=6

ii. Now, l² = r² + h²

∴ 10² = 6² + h²

∴ 100 = 36 + h²

∴ 100 – 36 = h²

∴ h² = 64

∴ h = √64 … [Taking square root on both sides]

= 8 cm

∴ The perpendicular height of the cone is 8 cm.