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Answer :
The formula for the volume of a cone is
[tex]$$
V = \frac{1}{3}\pi r^2 h.
$$[/tex]
Given that the volume is [tex]$147\pi$[/tex] cubic centimeters and the radius is [tex]$7$[/tex] cm, we substitute these values into the 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]
Since [tex]$\pi$[/tex] appears on both sides of the equation, it can be canceled out, leaving
[tex]$$
147 = \frac{1}{3}(49)h.
$$[/tex]
Thus, the expression that correctly represents the volume of the cone in terms of [tex]$h$[/tex] is
[tex]$$
147\pi = \frac{1}{3}\pi (7^2)h.
$$[/tex]
Among the options provided, the expression that matches this equation is option 2.
[tex]$$
V = \frac{1}{3}\pi r^2 h.
$$[/tex]
Given that the volume is [tex]$147\pi$[/tex] cubic centimeters and the radius is [tex]$7$[/tex] cm, we substitute these values into the 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]
Since [tex]$\pi$[/tex] appears on both sides of the equation, it can be canceled out, leaving
[tex]$$
147 = \frac{1}{3}(49)h.
$$[/tex]
Thus, the expression that correctly represents the volume of the cone in terms of [tex]$h$[/tex] is
[tex]$$
147\pi = \frac{1}{3}\pi (7^2)h.
$$[/tex]
Among the options provided, the expression that matches this equation is option 2.
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