Question
A cone with a radius of 6 ft and a height of 11 ft. Tarik finds the volume of the cone in the image. What is the volume of the cone in cubic units?(1 point)Responses396π cubic units396 pi cubic units66π cubic units66 pi cubic units132π cubic units132 pi cubic units242π cubic units242 pi cubic units
Answers
GPT-4o mini
The volume \( V \) of a cone can be calculated using the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height of the cone.
Given:
- Radius \( r = 6 \) ft
- Height \( h = 11 \) ft
Plugging in the values:
\[
V = \frac{1}{3} \pi (6)^2 (11)
\]
Calculating \( (6)^2 \):
\[
(6)^2 = 36
\]
Now substituting back:
\[
V = \frac{1}{3} \pi (36)(11)
\]
Calculating \( 36 \times 11 \):
\[
36 \times 11 = 396
\]
So now we have:
\[
V = \frac{1}{3} \pi (396)
\]
Calculating \( \frac{396}{3} \):
\[
\frac{396}{3} = 132
\]
Thus, the volume of the cone is:
\[
V = 132 \pi
\]
Therefore, the volume of the cone is **132π cubic units.**
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height of the cone.
Given:
- Radius \( r = 6 \) ft
- Height \( h = 11 \) ft
Plugging in the values:
\[
V = \frac{1}{3} \pi (6)^2 (11)
\]
Calculating \( (6)^2 \):
\[
(6)^2 = 36
\]
Now substituting back:
\[
V = \frac{1}{3} \pi (36)(11)
\]
Calculating \( 36 \times 11 \):
\[
36 \times 11 = 396
\]
So now we have:
\[
V = \frac{1}{3} \pi (396)
\]
Calculating \( \frac{396}{3} \):
\[
\frac{396}{3} = 132
\]
Thus, the volume of the cone is:
\[
V = 132 \pi
\]
Therefore, the volume of the cone is **132π cubic units.**