Circular Cone

Geometry Level 1

A pile of sand is in the form of a right circular cone with altitude 10 feet and slant height 30 feet. Find the ground area covered by the sand.

900pi 700pi 600pi 800pi

A Former Brilliant Member by A Former Brilliant Member

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1 solution

let r r be the radius of the base of the pile of sand

by Pythagorean Theorem ⟹ \implies r 2 = 3 0 2 − 1 0 2 = 800 r^2 = 30^2 - 10^2 = 800 ⟹ \implies r = 800 r = \sqrt{800}

solving for the area of the base ⟹ \implies A = π r 2 = π ( 800 ) 2 = A = \pi r^2 = \pi (\sqrt{800})^2 = 800 π \boxed{800\pi}

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