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Answer :
The formula for the volume of a cone is given by
[tex]$$
V = \frac{1}{3}\pi r^2 h.
$$[/tex]
Given that the radius is [tex]$7$[/tex] cm and the volume is [tex]$147\pi$[/tex] cubic centimeters, we substitute these values into the formula:
[tex]$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$[/tex]
Here is the step-by-step breakdown:
1. Start with the volume formula for a cone:
[tex]$$
V = \frac{1}{3}\pi r^2 h.
$$[/tex]
2. Substitute [tex]$r = 7$[/tex] cm into the formula:
[tex]$$
V = \frac{1}{3}\pi (7^2) h.
$$[/tex]
3. Since the volume [tex]$V$[/tex] is given as [tex]$147\pi$[/tex], the equation becomes:
[tex]$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$[/tex]
This is the expression that can be used to find [tex]$h$[/tex], the height of the cone.
Thus, the correct expression is
[tex]$$147\pi = \frac{1}{3}\pi(7^2)h.$$[/tex]
[tex]$$
V = \frac{1}{3}\pi r^2 h.
$$[/tex]
Given that the radius is [tex]$7$[/tex] cm and the volume is [tex]$147\pi$[/tex] cubic centimeters, we substitute these values into the formula:
[tex]$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$[/tex]
Here is the step-by-step breakdown:
1. Start with the volume formula for a cone:
[tex]$$
V = \frac{1}{3}\pi r^2 h.
$$[/tex]
2. Substitute [tex]$r = 7$[/tex] cm into the formula:
[tex]$$
V = \frac{1}{3}\pi (7^2) h.
$$[/tex]
3. Since the volume [tex]$V$[/tex] is given as [tex]$147\pi$[/tex], the equation becomes:
[tex]$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$[/tex]
This is the expression that can be used to find [tex]$h$[/tex], the height of the cone.
Thus, the correct expression is
[tex]$$147\pi = \frac{1}{3}\pi(7^2)h.$$[/tex]
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