To find the volume of a cone with a given radius and height, we use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone
- [tex]\( r \)[/tex] is the radius of the base of the cone
- [tex]\( h \)[/tex] is the height of the cone
- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159.
Given:
- Radius ([tex]\( r \)[/tex]) = 4 feet
- Height ([tex]\( h \)[/tex]) = 9 feet
1. First, we square the radius:
[tex]\[
r^2 = 4^2 = 16
\][/tex]
2. Next, we multiply this squared radius by the height:
[tex]\[
16 \times 9 = 144
\][/tex]
3. We then multiply the product by [tex]\(\pi\)[/tex]:
[tex]\[
144 \times \pi \approx 144 \times 3.14159 \approx 452.38934
\][/tex]
4. Finally, we take one-third of this product to find the volume:
[tex]\[
V \approx \frac{452.38934}{3} \approx 150.79645
\][/tex]
5. To match the required precision, we round this volume to two decimal places:
[tex]\[
V \approx 150.80
\][/tex]
So, the volume of the cone, rounded to two decimal places, is approximately [tex]\( 150.80 \)[/tex] cubic feet.
