How do you find the volume of a cone using an integral?

Sonny Malone

Sonny Malone

Answered question

2023-03-22

How to find the volume of a cone using an integral?

Answer & Explanation

Saottah87e

Saottah87e

Beginner2023-03-23Added 6 answers

A cone with base radius r and height h can be obtained by rotating the region under the line y = r h x about the x-axis from x=0 to x=h.
By Disk Method,
V = π 0 h ( r h x ) 2 d x = π r 2 h 2 0 h x 2 d x
by Power Rule,
= π r 2 h 2 [ x 3 3 ] 0 h = π r 2 h 2 h 3 3 = 1 3 π r 2 h

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