Answer :
The volume of a cone is given by the formula
[tex]$$
V = \frac{1}{3} \pi r^2 h.
$$[/tex]
Here, we are given that the volume is [tex]$147 \pi$[/tex] cubic centimeters and the radius is [tex]$7$[/tex] cm. Substituting these into the formula, we have
[tex]$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$[/tex]
Since [tex]$7^2 = 49$[/tex], the equation becomes
[tex]$$
147\pi = \frac{1}{3} \pi (49) h.
$$[/tex]
This equation is exactly the second expression provided:
[tex]$$
147 \pi=\frac{1}{3} \pi\left(7^2\right)(h).
$$[/tex]
To verify, we can cancel [tex]$\pi$[/tex] from both sides:
[tex]$$
147 = \frac{49}{3} h.
$$[/tex]
Multiplying both sides by [tex]$\frac{3}{49}$[/tex] gives
[tex]$$
h = \frac{147 \times 3}{49} = 9.
$$[/tex]
Thus, the correct expression that can be used to find [tex]$h$[/tex] is:
[tex]$$
147 \pi=\frac{1}{3} \pi\left(7^2\right)(h).
$$[/tex]
[tex]$$
V = \frac{1}{3} \pi r^2 h.
$$[/tex]
Here, we are given that the volume is [tex]$147 \pi$[/tex] cubic centimeters and the radius is [tex]$7$[/tex] cm. Substituting these into the formula, we have
[tex]$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$[/tex]
Since [tex]$7^2 = 49$[/tex], the equation becomes
[tex]$$
147\pi = \frac{1}{3} \pi (49) h.
$$[/tex]
This equation is exactly the second expression provided:
[tex]$$
147 \pi=\frac{1}{3} \pi\left(7^2\right)(h).
$$[/tex]
To verify, we can cancel [tex]$\pi$[/tex] from both sides:
[tex]$$
147 = \frac{49}{3} h.
$$[/tex]
Multiplying both sides by [tex]$\frac{3}{49}$[/tex] gives
[tex]$$
h = \frac{147 \times 3}{49} = 9.
$$[/tex]
Thus, the correct expression that can be used to find [tex]$h$[/tex] is:
[tex]$$
147 \pi=\frac{1}{3} \pi\left(7^2\right)(h).
$$[/tex]
