Question

The volume of a cylinder can be found using the formula V = pi r squared h.

Which is the correct first step in finding the height of a cylinder with a volume of 192 pi cubic inches and a radius of 5 inches?
5 = pi (192) squared h
V = pi + (5) squared + 192 pi
V = pi (5) squared (192)
192 pi = pi (5) squared h option 1 2 3 o r4

Answer 1

To find the height of a cylinder using the volume formula \( V = \pi r^2 h \) and given that the volume \( V = 192\pi \) cubic inches and the radius \( r = 5 \) inches, you want to isolate \( h \).

First, you substitute the known values into the formula:
\[
192\pi = \pi (5)^2 h
\]

Now, simplifying \( \pi (5)^2 \) gives you \( \pi \cdot 25 \), so:
\[
192\pi = 25\pi h
\]

To solve for \( h \), you can divide both sides by \( \pi \) (as long as \( \pi \neq 0 \)):
\[
192 = 25h
\]

Next, you would solve for \( h \) by dividing both sides by 25:
\[
h = \frac{192}{25}
\]

Now, looking at your options, the correct first step in isolating \( h \) from the initial formula would be:
\[
192\pi = \pi (5)^2 h
\]
This corresponds to your option:
- **Option 4:** \( 192\pi = \pi (5)^2 h \)

So, the correct first step is option 4.