Question

1. find the value of ( x ) given the volume. ( v = 6144pi ) units(^3)

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) (or \( x \) in this case) is the height. Here, the radius \( r = 16 \) and the volume \( V = 6144\pi \).

Step2: Substitute the known values into the formula

Substitute \( V = 6144\pi \), \( r = 16 \) into \( V = \pi r^2 x \):
\[
6144\pi = \pi (16)^2 x
\]

Step3: Simplify the equation

First, simplify \( (16)^2 = 256 \). Then, divide both sides of the equation by \( \pi \) (since \( \pi
eq 0 \)):
\[
6144 = 256x
\]

Step4: Solve for \( x \)

Divide both sides of the equation by 256:
\[
x = \frac{6144}{256} = 24
\]

Answer:

\( x = 24 \)