Question
The volume of a cylinder is approximately 72 feet cubed. Which is the best approximation of the volume of a cone with the same base and height as the cylinder?
24 feet cubed
216 feet cubed
24 pi feet cubed
216 pi feet cubed
24 feet cubed
216 feet cubed
24 pi feet cubed
216 pi feet cubed
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 with the same base and height is given by the formula:
\[
V' = \frac{1}{3} \pi r^2 h
\]
Since the cone has the same base and height as the cylinder, the relationship between the volumes can be expressed as:
\[
V' = \frac{1}{3} V
\]
Given that the volume of the cylinder is approximately 72 cubic feet, we can calculate the volume of the cone:
\[
V' = \frac{1}{3} \times 72 = 24 \text{ cubic feet}
\]
Thus, the best approximation of the volume of the cone with the same base and height as the cylinder is:
\[
\boxed{24} \text{ feet cubed}
\]
\[
V = \pi r^2 h
\]
The volume \( V' \) of a cone with the same base and height is given by the formula:
\[
V' = \frac{1}{3} \pi r^2 h
\]
Since the cone has the same base and height as the cylinder, the relationship between the volumes can be expressed as:
\[
V' = \frac{1}{3} V
\]
Given that the volume of the cylinder is approximately 72 cubic feet, we can calculate the volume of the cone:
\[
V' = \frac{1}{3} \times 72 = 24 \text{ cubic feet}
\]
Thus, the best approximation of the volume of the cone with the same base and height as the cylinder is:
\[
\boxed{24} \text{ feet cubed}
\]