To find the volume of a cone, we use the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Where:
- [tex]\( r \)[/tex] is the radius of the base
- [tex]\( h \)[/tex] is the height of the cone
- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14159
Given:
- Radius ([tex]\( r \)[/tex]) = 6 feet
- Height ([tex]\( h \)[/tex]) = 10 feet
First, we square the radius:
[tex]\[ r^2 = 6^2 = 36 \][/tex]
Next, we multiply this result by the height:
[tex]\[ 36 \times 10 = 360 \][/tex]
Then, we multiply this product by [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[ \frac{1}{3} \times 360 = 120 \][/tex]
Finally, we include [tex]\( \pi \)[/tex] in the result:
[tex]\[ V = 120 \pi \][/tex]
Thus, the volume of the cone is:
[tex]\[ 120 \pi \, \text{cubic feet} \][/tex]
This means that the volume of the cone, expressed in terms of [tex]\( \pi \)[/tex], is [tex]\( 120 \pi \)[/tex] cubic feet.
