Question
The volume of the right cylinder = 90π ft3
with a height of 10 feet.
Check TWO answers that are true.
(2 points)
Responses
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.
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.
The axis of the oblique cylinder is equal to the height of the right cylinder.
The axis of the oblique cylinder is equal to the height of the right cylinder.
The radius of the right cylinder = 9 feet
The radius of the right cylinder = 9 feet
The radius of the right cylinder is about 1.7 feet
The radius of the right cylinder is about 1.7 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.
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.
The radius of the right cylinder = 3 feet
The radius of the right cylinder = 3 feet
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Answers
GPT-4o mini
To find the radius of the right cylinder with a volume of \(90\pi\) cubic feet and a height of \(10\) feet, we can use the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
Where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height.
Given \(V = 90\pi\) and \(h = 10\), we can set up the equation:
\[
90\pi = \pi r^2 (10)
\]
Dividing both sides by \(\pi\):
\[
90 = r^2 (10)
\]
Then, dividing both sides by \(10\):
\[
9 = r^2
\]
Taking the square root of both sides gives:
\[
r = 3
\]
So the radius of the right cylinder is \(3\) feet.
Now let's evaluate the statements given:
1. **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 radius and height (or altitude) are the same, the volumes of the oblique and right cylinders are equal.
2. **The axis of the oblique cylinder is equal to the height of the right cylinder.**
- This statement can be **TRUE** if specifically referring to an oblique cylinder whose slant height is equal to the vertical height of the right cylinder.
3. **The radius of the right cylinder = 9 feet.**
- This statement is **FALSE**. The radius is \(3\) feet, not \(9\) feet.
4. **The radius of the right cylinder is about 1.7 feet.**
- This statement is **FALSE**. The radius is \(3\) feet, not \(1.7\) feet.
5. **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**. If the height (or altitude) and radius are equal, their volumes are equal.
6. **The radius of the right cylinder = 3 feet.**
- This statement is **TRUE**. We calculated that the radius is indeed \(3\) feet.
Based on this analysis, the two true statements are:
- **The axis of the oblique cylinder is equal to the height of the right cylinder.**
- **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.**
- **The radius of the right cylinder = 3 feet.**
Since you asked for TWO answers that are true, the most relevant ones are the last two:
- **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.**
\[
V = \pi r^2 h
\]
Where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height.
Given \(V = 90\pi\) and \(h = 10\), we can set up the equation:
\[
90\pi = \pi r^2 (10)
\]
Dividing both sides by \(\pi\):
\[
90 = r^2 (10)
\]
Then, dividing both sides by \(10\):
\[
9 = r^2
\]
Taking the square root of both sides gives:
\[
r = 3
\]
So the radius of the right cylinder is \(3\) feet.
Now let's evaluate the statements given:
1. **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 radius and height (or altitude) are the same, the volumes of the oblique and right cylinders are equal.
2. **The axis of the oblique cylinder is equal to the height of the right cylinder.**
- This statement can be **TRUE** if specifically referring to an oblique cylinder whose slant height is equal to the vertical height of the right cylinder.
3. **The radius of the right cylinder = 9 feet.**
- This statement is **FALSE**. The radius is \(3\) feet, not \(9\) feet.
4. **The radius of the right cylinder is about 1.7 feet.**
- This statement is **FALSE**. The radius is \(3\) feet, not \(1.7\) feet.
5. **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**. If the height (or altitude) and radius are equal, their volumes are equal.
6. **The radius of the right cylinder = 3 feet.**
- This statement is **TRUE**. We calculated that the radius is indeed \(3\) feet.
Based on this analysis, the two true statements are:
- **The axis of the oblique cylinder is equal to the height of the right cylinder.**
- **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.**
- **The radius of the right cylinder = 3 feet.**
Since you asked for TWO answers that are true, the most relevant ones are the last two:
- **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.**