Question

The volume of a cone with a radius of 7 cm is 147 cubic centimeters. Which expression can be used to find h, the height ofthe cone?147 R72 (h)O 147a147

Answer 1

The choices are not attached but we can solve the problem from the given information

Answer:

The expression can be used to find h is  $h=\frac{3V}{\pi r^{2}}$

The height of the cone is $\frac{9}{\pi }$ cm

Step-by-step explanation:

The formula of the volume of the cone is V = $\frac{1}{3}$ π r² h, where

• r is the radius of its base
• h is the height of it

Let us find the height of the cone from the formula of its volume

∵ V = $\frac{1}{3}$ π r² h

- Multiply both sides by 3

∴ 3 V = π r² h

- Divide both sides by π r²

∴ $\frac{3V}{\pi r^{2}}=h$

- Switch the two sides

∴ $h=\frac{3V}{\pi r^{2}}$

The expression can be used to find h is  $h=\frac{3V}{\pi r^{2}}$

∵ The radius of the cone is 7 cm

∴ r = 7

∵ The volume of the cone is 147 cm³

∴ V = 147

- Substitute them in the expression of the height to find it

∵  $h=\frac{3(147)}{\pi (7)^{2}}$

∴ h = $\frac{9}{\pi }$ cm

The height of the cone is $\frac{9}{\pi }$ cm