Consider a right circular cone whose base is a disk of radius 10cm. In its development figure, the central angle of the sector is 240. Find the height of the right circular cone.

Answer 1

θ = 240° = 4π/3, r = 10, L = the slant height, h = the height

Let h be the height so that h, L and r form a a right triangle.

L² = r²+h²

A cone is formed by folding the sector's edges together. The edges are the slant height of the cone, L.

θ = 2πr/L This is because, when folded, the arc makes a full circle of the base of the cone or 2π so the length of the arc is 2πr

L = 2πr/θ = 2π(10)/(4π/3) = 15 cm

h = √(L²-r²) = √(225 - 100) = √125 = 5√5 cm

Answer 2

Let radius of sector is l. Then 2πl·240°/360° = 2πr, 2/3l = r; l = 3/2r = 15 cm.

By Pyrhagorian THeorem h = √15² - 10² = √125 = 5√5 cm ≈ 11.18 cm