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Answer :
To determine the height [tex]$h$[/tex] of the cone, we start with the formula for the volume of a cone:
[tex]$$
V = \frac{1}{3} \pi r^2 h.
$$[/tex]
We are given:
- The volume: [tex]$V = 147 \pi$[/tex] cubic centimeters,
- The radius: [tex]$r = 7$[/tex] cm.
Substitute these values into the volume formula:
[tex]$$
147 \pi = \frac{1}{3} \pi (7)^2 \, h.
$$[/tex]
Notice that [tex]$7^2 = 49$[/tex], so the equation becomes:
[tex]$$
147 \pi = \frac{1}{3} \pi (49) \, h.
$$[/tex]
This equation corresponds to the expression:
[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]
Thus, the correct expression to find [tex]$h$[/tex] is:
[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]
Now, we solve for [tex]$h$[/tex]:
1. Cancel [tex]$\pi$[/tex] from both sides (since [tex]$\pi \neq 0$[/tex]):
[tex]$$
147 = \frac{1}{3} (49) \, h.
$$[/tex]
2. Multiply both sides by [tex]$3$[/tex] to eliminate the fraction:
[tex]$$
441 = 49h.
$$[/tex]
3. Divide both sides by [tex]$49$[/tex]:
[tex]$$
h = \frac{441}{49} = 9.
$$[/tex]
So, the height of the cone is [tex]$9$[/tex] cm.
Therefore, the correct expression is:
[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]
[tex]$$
V = \frac{1}{3} \pi r^2 h.
$$[/tex]
We are given:
- The volume: [tex]$V = 147 \pi$[/tex] cubic centimeters,
- The radius: [tex]$r = 7$[/tex] cm.
Substitute these values into the volume formula:
[tex]$$
147 \pi = \frac{1}{3} \pi (7)^2 \, h.
$$[/tex]
Notice that [tex]$7^2 = 49$[/tex], so the equation becomes:
[tex]$$
147 \pi = \frac{1}{3} \pi (49) \, h.
$$[/tex]
This equation corresponds to the expression:
[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]
Thus, the correct expression to find [tex]$h$[/tex] is:
[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]
Now, we solve for [tex]$h$[/tex]:
1. Cancel [tex]$\pi$[/tex] from both sides (since [tex]$\pi \neq 0$[/tex]):
[tex]$$
147 = \frac{1}{3} (49) \, h.
$$[/tex]
2. Multiply both sides by [tex]$3$[/tex] to eliminate the fraction:
[tex]$$
441 = 49h.
$$[/tex]
3. Divide both sides by [tex]$49$[/tex]:
[tex]$$
h = \frac{441}{49} = 9.
$$[/tex]
So, the height of the cone is [tex]$9$[/tex] cm.
Therefore, the correct expression is:
[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]
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