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 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 is about 1.7 feet
The radius of the right cylinder is about 1.7 feet
The radius of the right cylinder = 3 feet
The radius of the right cylinder = 3 feet
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 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 radius of the right cylinder = 9 feet
with a height of 10 feet.
Check TWO answers that are true.
(2 points)
Responses
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 is about 1.7 feet
The radius of the right cylinder is about 1.7 feet
The radius of the right cylinder = 3 feet
The radius of the right cylinder = 3 feet
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 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 radius of the right cylinder = 9 feet
Answers
GPT-4o mini
To determine which statements are true, we can start by calculating the radius of the right cylinder using its volume formula.
The volume \( V \) of a right cylinder is given by the formula:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height. In this case, we know:
\[
V = 90\pi \text{ ft}^3
\]
\[
h = 10 \text{ ft}
\]
We can set up the equation:
\[
90\pi = \pi r^2 (10)
\]
Dividing both sides by \( \pi \):
\[
90 = 10r^2
\]
Dividing both sides by 10 gives:
\[
r^2 = 9
\]
Taking the square root of both sides:
\[
r = 3 \text{ ft}
\]
Now, we can analyze the provided statements:
1. **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.**
- **True**. Both types of cylinders maintain the same volume if they have the same radius and height (altitude).
2. **The radius of the right cylinder is about 1.7 feet.**
- **False**. We calculated the radius to be 3 feet.
3. **The radius of the right cylinder = 3 feet.**
- **True**. We calculated that the radius is indeed 3 feet.
4. **The axis of the oblique cylinder is equal to the height of the right cylinder.**
- **False**. The axis of an oblique cylinder may not be the same as the vertical height of the cylinder; it could be longer depending on the tilt.
5. **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.**
- **False**. If they have the same radius and height (altitude), they will have the same volume.
6. **The radius of the right cylinder = 9 feet.**
- **False**. The radius has been calculated to be 3 feet.
### Summary of True Responses:
- 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.
So the two correct answers are:
1. 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.
2. The radius of the right cylinder = 3 feet.
The volume \( V \) of a right cylinder is given by the formula:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height. In this case, we know:
\[
V = 90\pi \text{ ft}^3
\]
\[
h = 10 \text{ ft}
\]
We can set up the equation:
\[
90\pi = \pi r^2 (10)
\]
Dividing both sides by \( \pi \):
\[
90 = 10r^2
\]
Dividing both sides by 10 gives:
\[
r^2 = 9
\]
Taking the square root of both sides:
\[
r = 3 \text{ ft}
\]
Now, we can analyze the provided statements:
1. **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.**
- **True**. Both types of cylinders maintain the same volume if they have the same radius and height (altitude).
2. **The radius of the right cylinder is about 1.7 feet.**
- **False**. We calculated the radius to be 3 feet.
3. **The radius of the right cylinder = 3 feet.**
- **True**. We calculated that the radius is indeed 3 feet.
4. **The axis of the oblique cylinder is equal to the height of the right cylinder.**
- **False**. The axis of an oblique cylinder may not be the same as the vertical height of the cylinder; it could be longer depending on the tilt.
5. **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.**
- **False**. If they have the same radius and height (altitude), they will have the same volume.
6. **The radius of the right cylinder = 9 feet.**
- **False**. The radius has been calculated to be 3 feet.
### Summary of True Responses:
- 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.
So the two correct answers are:
1. 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.
2. The radius of the right cylinder = 3 feet.