High School

The volume of a cone with a radius of 7 cm is [tex]147 \pi[/tex] cubic centimeters. Which expression can be used to find [tex]h[/tex], the height of the cone?

A. [tex]147 \pi = \frac{1}{3} \pi (7)^2 (h)[/tex]
B. [tex]147 \pi = \frac{1}{3} \pi \left[7^2\right] (h)[/tex]
C. [tex]147 \pi = \frac{1}{3} \pi (7) (h)[/tex]

(Note: Correct options to match the formula for the volume of a cone, [tex]V = \frac{1}{3} \pi r^2 h[/tex])

Answer :

The volume of a cone is given by the formula

[tex]$$
V = \frac{1}{3}\pi r^2h.
$$[/tex]

We are provided with a volume of [tex]$147\pi$[/tex] cubic centimeters and a radius [tex]$r = 7$[/tex] cm. Substituting these values into the formula gives

[tex]$$
147\pi = \frac{1}{3}\pi (7)^2 h.
$$[/tex]

Notice that [tex]$(7)^2$[/tex] is [tex]$49$[/tex], so the equation becomes

[tex]$$
147\pi = \frac{1}{3}\pi \cdot 49 \cdot h.
$$[/tex]

The correct expression to find [tex]$h$[/tex] is

[tex]$$
147\pi = \frac{1}{3}\pi\left[7^2\right](h).
$$[/tex]

Thus, the appropriate multiple-choice option is the second one.