To find the radius of the right cylinder, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Given that the volume \( V = 90\pi \) cubic feet and height \( h = 10 \) feet, we can set up the equation:
\[ 90\pi = \pi r^2 \times 10 \]
Dividing both sides by \( \pi \):
\[ 90 = r^2 \times 10 \]
Now divide both sides by 10:
\[ r^2 = 9 \]
Taking the square root of both sides:
\[ r = 3 \text{ feet} \]
Now we can evaluate the given statements:
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The axis of the oblique cylinder is equal to the height of the right cylinder.
- This statement is not necessarily true; the oblique cylinder can have a different height.
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The radius of the right cylinder = 9 feet.
- This statement is false because we found the radius to be 3 feet.
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The radius of the right cylinder is about 1.7 feet.
- This statement is false; the radius is 3 feet.
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The radius of the right cylinder = 3 feet.
- This statement is true as calculated.
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The oblique cylinder does not have the same volume as the right cylinder with the altitude = the height and the radius the same for both.
- This statement is false. If the oblique cylinder has the same radius and the same height (altitude), it will indeed have the same volume.
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The oblique cylinder and the right cylinder would have the same volume as long as the height = the altitude and they have the same radius.
- This statement is true.
Therefore, the two true statements are:
- The radius of the right cylinder = 3 feet.
- The oblique cylinder and the right cylinder would have the same volume as long as the height = the altitude and they have the same radius.