To find the volume of a cone with a radius of 6 cm and a height of 10 cm, we will use the formula for the volume of a cone, which is given by:
[tex]\[ V = \frac{\pi r^2 h}{3} \][/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.
Substituting the given values into the formula:
- [tex]\( r = 6 \)[/tex] cm,
- [tex]\( h = 10 \)[/tex] cm,
[tex]\[
V = \frac{\pi (6)^2 (10)}{3}
\][/tex]
First, we calculate the square of the radius:
[tex]\[
6^2 = 36
\][/tex]
Then, we multiply this result by the height:
[tex]\[
36 \times 10 = 360
\][/tex]
Now, we divide by 3 to get the volume:
[tex]\[
\frac{360}{3} = 120
\][/tex]
Hence, the volume of the cone is:
[tex]\[
120 \pi \text{ cm}^3
\][/tex]
So, the correct answer is:
(C) [tex]\( 120 \pi \text{ cm}^3 \)[/tex]
