Question
Find the radius of a cylinder that has a height of 4 and a volume of 81π cubic units.(1 point)
Responses
20.25 units
20.25 units
10.125 units
10.125 units
4.5 units
4.5 units
9 units
Responses
20.25 units
20.25 units
10.125 units
10.125 units
4.5 units
4.5 units
9 units
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the radius of a cylinder given its height and volume, we use the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.
In this case, the volume \(V = 81\pi\) cubic units and the height \(h = 4\) units. Plugging these values into the volume formula, we get:
\[
81\pi = \pi r^2 (4)
\]
We can simplify this equation by dividing both sides by \(\pi\):
\[
81 = r^2 (4)
\]
Now, divide both sides by 4:
\[
r^2 = \frac{81}{4}
\]
Taking the square root of both sides to find \(r\):
\[
r = \sqrt{\frac{81}{4}} = \frac{\sqrt{81}}{\sqrt{4}} = \frac{9}{2} = 4.5
\]
The radius of the cylinder is \(4.5\) units.
Therefore, the correct response is:
**4.5 units**.
\[
V = \pi r^2 h
\]
where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.
In this case, the volume \(V = 81\pi\) cubic units and the height \(h = 4\) units. Plugging these values into the volume formula, we get:
\[
81\pi = \pi r^2 (4)
\]
We can simplify this equation by dividing both sides by \(\pi\):
\[
81 = r^2 (4)
\]
Now, divide both sides by 4:
\[
r^2 = \frac{81}{4}
\]
Taking the square root of both sides to find \(r\):
\[
r = \sqrt{\frac{81}{4}} = \frac{\sqrt{81}}{\sqrt{4}} = \frac{9}{2} = 4.5
\]
The radius of the cylinder is \(4.5\) units.
Therefore, the correct response is:
**4.5 units**.
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