Question
The volume of a cylinder is 60 cm3 . What is the volume of a cone that shares the same radius and height as the cylinder?(1 point) Responses 20 cm3 20 cm3 - no response given 90 cm3 90 cm3 - incorrect 180 cm3 180 cm3 - no response given 40 cm3
Answers
GPT-4o mini
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
The volume \( V \) of a cone is given by the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
If the cylinder has a volume of 60 cm³, that means:
\[
\pi r^2 h = 60 \text{ cm}^3
\]
To find the volume of the cone with the same radius and height, we use the cone's volume formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
Substituting the expression for the cylinder's volume:
\[
V = \frac{1}{3} \times 60 \text{ cm}^3
\]
Calculating this gives:
\[
V = 20 \text{ cm}^3
\]
Thus, the volume of the cone that shares the same radius and height as the cylinder is \( \boxed{20 \text{ cm}^3} \).
\[
V = \pi r^2 h
\]
The volume \( V \) of a cone is given by the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
If the cylinder has a volume of 60 cm³, that means:
\[
\pi r^2 h = 60 \text{ cm}^3
\]
To find the volume of the cone with the same radius and height, we use the cone's volume formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
Substituting the expression for the cylinder's volume:
\[
V = \frac{1}{3} \times 60 \text{ cm}^3
\]
Calculating this gives:
\[
V = 20 \text{ cm}^3
\]
Thus, the volume of the cone that shares the same radius and height as the cylinder is \( \boxed{20 \text{ cm}^3} \).