The volume of a cone is 84pi cubic inches. If the radius of the cone is 6 inches determine its height

Question

asked Apr 9, 2021 60.1k views

1 Answer

Ostap Brehin · Answer 1 · 2021-04-14T19:27:25+0000

Answer:

7 inches

Explanation:

Given

Shape: Cone

$Volume = 84\pi in^3$

Radius = 6in

Required

Determine the height

Volume of a cone is:

$V = (1)/(3)\pi r^2h$

Substitute values for volume and radius

$84\pi = (1)/(3)\pi * 6^2 * h$

$84\pi = (1)/(3)\pi * 36 * h$

$84\pi = (36)/(3)\pi* h$

$84\pi = 12\pi* h$

Solve for h

$h = (84\pi)/(12\pi)$

h = 7

Hence:

The height is 7 inches