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 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 = 9 feet
The radius of the right cylinder = 9 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 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 = 3 feet
Answers
GPT-4o mini
To find the correct answers, let's start by calculating the radius of the right cylinder based on the given volume and height.
The formula for the volume \( V \) of a right cylinder is given by:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
Given:
- \( V = 90\pi \, \text{ft}^3 \)
- \( h = 10 \, \text{ft} \)
Substituting the given values into the volume formula:
\[
90\pi = \pi r^2 (10)
\]
We can divide both sides by \( \pi \):
\[
90 = 10r^2
\]
Next, divide both sides by 10:
\[
9 = r^2
\]
Taking the square root of both sides:
\[
r = 3
\]
So, the radius of the right cylinder is 3 feet.
Now, let's evaluate the statements:
1. **The radius of the right cylinder is about 1.7 feet.** (False)
2. **The radius of the right cylinder = 9 feet.** (False)
3. **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)
4. **The axis of the oblique cylinder is equal to the height of the right cylinder.** (False)
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)
6. **The radius of the right cylinder = 3 feet.** (True)
Thus, the two true statements are:
- 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 formula for the volume \( V \) of a right cylinder is given by:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
Given:
- \( V = 90\pi \, \text{ft}^3 \)
- \( h = 10 \, \text{ft} \)
Substituting the given values into the volume formula:
\[
90\pi = \pi r^2 (10)
\]
We can divide both sides by \( \pi \):
\[
90 = 10r^2
\]
Next, divide both sides by 10:
\[
9 = r^2
\]
Taking the square root of both sides:
\[
r = 3
\]
So, the radius of the right cylinder is 3 feet.
Now, let's evaluate the statements:
1. **The radius of the right cylinder is about 1.7 feet.** (False)
2. **The radius of the right cylinder = 9 feet.** (False)
3. **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)
4. **The axis of the oblique cylinder is equal to the height of the right cylinder.** (False)
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)
6. **The radius of the right cylinder = 3 feet.** (True)
Thus, the two true statements are:
- 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.