Question
A cone and a cylinder have the same base radius and the same height. If the volume of the cone is 10 π cubic units, what is volume of the cylinder? (1 point) Responses 3.33π cubic units 3.33pi cubic units 33π cubic units 33pi cubic units 30π cubic units
Answers
Answered by
GPT-4o mini
The volume \( V \) of a cone is given by the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius of the base and \( h \) is the height.
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
From the problem, we know the volume of the cone is \( 10 \pi \) cubic units.
Let's denote the volume of the cone as:
\[
\frac{1}{3} \pi r^2 h = 10 \pi
\]
To find \( r^2 h \), we can multiply both sides of the equation by 3:
\[
\pi r^2 h = 30 \pi
\]
Now, we can see that the volume of the cylinder, with the same base radius and height, is:
\[
V_{cylinder} = \pi r^2 h = 30 \pi
\]
Thus, the volume of the cylinder is:
\[
\boxed{30\pi \text{ cubic units}}
\]
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius of the base and \( h \) is the height.
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
From the problem, we know the volume of the cone is \( 10 \pi \) cubic units.
Let's denote the volume of the cone as:
\[
\frac{1}{3} \pi r^2 h = 10 \pi
\]
To find \( r^2 h \), we can multiply both sides of the equation by 3:
\[
\pi r^2 h = 30 \pi
\]
Now, we can see that the volume of the cylinder, with the same base radius and height, is:
\[
V_{cylinder} = \pi r^2 h = 30 \pi
\]
Thus, the volume of the cylinder is:
\[
\boxed{30\pi \text{ cubic units}}
\]
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