Answer :
We start with the formula for the volume of a cone:
[tex]$$
V = \frac{1}{3} \pi r^2 h.
$$[/tex]
The problem gives us a cone with radius [tex]$r=7\text{ cm}$[/tex] and volume [tex]$147\pi\text{ cm}^3$[/tex]. Substituting these values into the formula, we get:
[tex]$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$[/tex]
Notice here that [tex]$7^2 = 49$[/tex], so the equation becomes:
[tex]$$
147\pi = \frac{1}{3} \pi \cdot 49 \cdot h.
$$[/tex]
This matches the expression in the second option:
[tex]$$
147 \pi=\frac{1}{3} \pi\left(7^2\right)(h).
$$[/tex]
Thus, the correct option is the second one.
Next, if we wish to solve for [tex]$h$[/tex], we cancel [tex]$\pi$[/tex] from both sides:
[tex]$$
147 = \frac{1}{3} \cdot 49 \cdot h.
$$[/tex]
Multiply both sides by [tex]$3$[/tex] to eliminate the fraction:
[tex]$$
441 = 49h.
$$[/tex]
Then, divide both sides by [tex]$49$[/tex]:
[tex]$$
h = \frac{441}{49} = 9.
$$[/tex]
So, the height of the cone is [tex]$9\text{ cm}$[/tex], and the correct choice is option 2.
[tex]$$
V = \frac{1}{3} \pi r^2 h.
$$[/tex]
The problem gives us a cone with radius [tex]$r=7\text{ cm}$[/tex] and volume [tex]$147\pi\text{ cm}^3$[/tex]. Substituting these values into the formula, we get:
[tex]$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$[/tex]
Notice here that [tex]$7^2 = 49$[/tex], so the equation becomes:
[tex]$$
147\pi = \frac{1}{3} \pi \cdot 49 \cdot h.
$$[/tex]
This matches the expression in the second option:
[tex]$$
147 \pi=\frac{1}{3} \pi\left(7^2\right)(h).
$$[/tex]
Thus, the correct option is the second one.
Next, if we wish to solve for [tex]$h$[/tex], we cancel [tex]$\pi$[/tex] from both sides:
[tex]$$
147 = \frac{1}{3} \cdot 49 \cdot h.
$$[/tex]
Multiply both sides by [tex]$3$[/tex] to eliminate the fraction:
[tex]$$
441 = 49h.
$$[/tex]
Then, divide both sides by [tex]$49$[/tex]:
[tex]$$
h = \frac{441}{49} = 9.
$$[/tex]
So, the height of the cone is [tex]$9\text{ cm}$[/tex], and the correct choice is option 2.
