To find the volume of a cone with a given height and radius, we use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Where:
- \( V \) is the volume of the cone,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone, and
- \( \pi \) (pi) is approximately 3.14159.
Given:
- Height \( h = 27 \) cm,
- Radius \( r = 13 \) cm.
Let's go through the steps to find the volume:
1. Square the radius: Calculate \( r^2 \):
[tex]\[
13^2 = 169
\][/tex]
2. Multiply by the height:
[tex]\[
r^2 \times h = 169 \times 27 = 4563
\][/tex]
3. Multiply by pi (\( \pi \)):
[tex]\[
4563 \times \pi \approx 4563 \times 3.14159 \approx 14335.087
\][/tex]
4. Divide by 3 to find the volume:
[tex]\[
V = \frac{14335.087}{3} \approx 4778.362
\][/tex]
5. Round to the nearest tenth:
[tex]\[
V \approx 4778.4
\][/tex]
So, the volume of the cone is approximately [tex]\( 4778.4 \text{ cm}^3 \)[/tex].
