Question
A cone is shown with the height 6in and radius 2in
What is the volume of the cone in terms of π?
Responses
A 8π
8π in^3
B 16π
16π in^3
C 24π
24π in^3
D 32π in^3
What is the volume of the cone in terms of π?
Responses
A 8π
8π in^3
B 16π
16π in^3
C 24π
24π in^3
D 32π in^3
Answers
Answered by
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. In this case, the radius \( r \) is 2 inches and the height \( h \) is 6 inches.
Substituting the values into the formula:
\[
V = \frac{1}{3} \pi (2)^2 (6)
\]
Calculating the radius squared:
\[
(2)^2 = 4
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \pi (4)(6)
\]
Calculating \( 4 \times 6 \):
\[
4 \times 6 = 24
\]
So, the volume becomes:
\[
V = \frac{1}{3} \pi (24) = 8\pi
\]
Thus, the volume of the cone is:
\[
\text{Volume} = 8\pi \, \text{in}^3
\]
The correct response is **A: 8π in³**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height of the cone. In this case, the radius \( r \) is 2 inches and the height \( h \) is 6 inches.
Substituting the values into the formula:
\[
V = \frac{1}{3} \pi (2)^2 (6)
\]
Calculating the radius squared:
\[
(2)^2 = 4
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \pi (4)(6)
\]
Calculating \( 4 \times 6 \):
\[
4 \times 6 = 24
\]
So, the volume becomes:
\[
V = \frac{1}{3} \pi (24) = 8\pi
\]
Thus, the volume of the cone is:
\[
\text{Volume} = 8\pi \, \text{in}^3
\]
The correct response is **A: 8π in³**.