Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ The volume of a cone with a radius of 7 cm is [tex]147 \pi[/tex] cubic centimeters. Which expression can be used to find [tex]h[/tex], the height of the cone?

A. [tex]147 \pi = \frac{1}{3}(7)(h)^2[/tex]

B. [tex]147 \pi = \frac{1}{3} \pi(7^2)(h)[/tex]

C. [tex]147 \pi = \frac{1}{3} \pi h[/tex]

D. [tex]147 \pi = \frac{1}{3} \pi(7)(h)[/tex]

To solve the problem, start with the formula for the volume of a cone:

[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, substitute these values into the formula:

[tex]$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$[/tex]

Simplify the expression:

1. Compute [tex]$7^2$[/tex]:
[tex]$$
7^2 = 49.
$$[/tex]

2. Now the equation becomes:
[tex]$$
147\pi = \frac{1}{3}\pi (49) h.
$$[/tex]

This is the correct expression that relates the volume, the radius, and the height of the cone.

To verify the height, you can solve for [tex]$h$[/tex]:

- Cancel the common factor [tex]$\pi$[/tex] on both sides:

[tex]$$
147 = \frac{49}{3} h.
$$[/tex]

- Multiply both sides by [tex]$3$[/tex] to eliminate the fraction:

[tex]$$
441 = 49h.
$$[/tex]

- Divide both sides by [tex]$49$[/tex]:

[tex]$$
h = \frac{441}{49} = 9.
$$[/tex]

Thus, the height of the cone is [tex]$9$[/tex] cm.

The corresponding expression used to find [tex]$h$[/tex] is:

[tex]$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$[/tex]

So the correct answer is the expression in the second option.