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

1 answer

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:

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