Question

Find the height of the figure with the volume Vequals=32403240piπ cubic cm. the radius is 9

Answer 1

To find the height of a cylindrical figure given the volume \( V \), radius \( r \), and that the volume is given by the formula:

\[
V = \pi r^2 h
\]

we can rearrange this formula to solve for the height \( h \):

\[
h = \frac{V}{\pi r^2}
\]

Given:
- Volume \( V = 32403240\pi \) cubic cm
- Radius \( r = 9 \) cm

First, we need to calculate \( \pi r^2 \):

\[
r^2 = 9^2 = 81
\]

So,

\[
\pi r^2 = \pi \times 81
\]

Now, substituting this into the formula for height:

\[
h = \frac{32403240\pi}{\pi \times 81}
\]

The \( \pi \) in the numerator and denominator cancel out:

\[
h = \frac{32403240}{81}
\]

Now, we need to perform the division:

\[
h = 400400
\]

Thus, the height of the figure is:

\[
\boxed{400400} \text{ cm}
\]