Answer:
7 inches
Step-by-step explanation:
Given
Shape: Cone
[tex]Volume = 84\pi in^3[/tex]
[tex]Radius = 6in[/tex]
Required
Determine the height
Volume of a cone is:
[tex]V = \frac{1}{3}\pi r^2h[/tex]
Substitute values for volume and radius
[tex]84\pi = \frac{1}{3}\pi * 6^2 * h[/tex]
[tex]84\pi = \frac{1}{3}\pi * 36 * h[/tex]
[tex]84\pi = \frac{36}{3}\pi* h[/tex]
[tex]84\pi = 12\pi* h[/tex]
Solve for h
[tex]h = \frac{84\pi}{12\pi}[/tex]
[tex]h = 7[/tex]
Hence:
The height is 7 inches
