Question

The volume of a cone is 261.8 cm cubed and the height of the cone is 10 cm. What is the approximate radius of the cone?



Use the `\pi` button in your calculations and round to the nearest whole.

Answer 1

The formula for the volume \( V \) of a cone is given by:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height of the cone. We know the volume \( V = 261.8 \, \text{cm}^3 \) and the height \( h = 10 \, \text{cm} \). We need to solve for the radius \( r \).

Substituting the known values into the volume formula, we have:

\[
261.8 = \frac{1}{3} \pi r^2 (10)
\]

This simplifies to:

\[
261.8 = \frac{10}{3} \pi r^2
\]

Now, multiply both sides by \( 3 \) to eliminate the fraction:

\[
3 \times 261.8 = 10 \pi r^2
\]

This results in:

\[
785.4 = 10 \pi r^2
\]

Next, divide both sides by \( 10 \pi \):

\[
\frac{785.4}{10 \pi} = r^2
\]

Calculating \( \frac{785.4}{10} = 78.54 \), we have:

\[
r^2 = \frac{78.54}{\pi}
\]

Now, using \( \pi \approx 3.14 \):

\[
r^2 = \frac{78.54}{3.14} \approx 25
\]

Taking the square root of both sides gives:

\[
r \approx \sqrt{25} \approx 5
\]

Thus, the approximate radius of the cone is:

\[
\boxed{5} \, \text{cm}
\]