Question

Find the height of a cone when its diameter is 8 inches and the volume is 100 cubic inches

Answer 1

Answer:

$\frac{75}{4\pi }$ inches or approximately 5.97 inches  

Step-by-step explanation:

Use the cone volume formula: V = $\pi$r²$\frac{h}{3}$

The diameter is 8 inches, so the radius will be 4 inches.

Plug in the radius and volume, and solve for h

V = $\pi$r²$\frac{h}{3}$

100 = $\pi$(4²)($\frac{h}{3}$)

100 = 16$\pi$$\frac{h}{3}$

Divide each side by 16$\pi$

$\frac{25}{4\pi }$ = $\frac{h}{3}$

Cross multiply and solve for h:

4$\pi$h = 75

h = $\frac{75}{4\pi }$

So, the cone's height is $\frac{75}{4\pi }$ or approximately 5.97 inches