Question
Rita has a circular hot tub. The hot tub has a diameter of 10 feet. It is 3.5 feet deep. How much water can the hot tub hold?(1 point)
cubic feet
cubic feet
Answers
GPT-4o mini
To find out how much water the circular hot tub can hold, we need to calculate the volume of a cylinder since the hot tub can be approximated as a cylinder.
The formula for the volume \( V \) of a cylinder is:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (or depth) of the cylinder, and
- \( \pi \) is approximately 3.14.
1. **Find the radius:**
The diameter of the hot tub is 10 feet, so the radius \( r \) is half of the diameter:
\[
r = \frac{10}{2} = 5 \text{ feet}
\]
2. **Determine the depth (height):**
The depth \( h \) of the hot tub is given as 3.5 feet.
3. **Calculate the volume:**
Substitute the values into the volume formula:
\[
V = \pi (5^2) (3.5)
\]
\[
V = \pi (25) (3.5)
\]
\[
V = 87.5\pi
\]
Now, using \( \pi \approx 3.14 \):
\[
V \approx 87.5 \times 3.14 \approx 274.375 \text{ cubic feet}
\]
Thus, the hot tub can hold approximately **274.375 cubic feet** of water.
The formula for the volume \( V \) of a cylinder is:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (or depth) of the cylinder, and
- \( \pi \) is approximately 3.14.
1. **Find the radius:**
The diameter of the hot tub is 10 feet, so the radius \( r \) is half of the diameter:
\[
r = \frac{10}{2} = 5 \text{ feet}
\]
2. **Determine the depth (height):**
The depth \( h \) of the hot tub is given as 3.5 feet.
3. **Calculate the volume:**
Substitute the values into the volume formula:
\[
V = \pi (5^2) (3.5)
\]
\[
V = \pi (25) (3.5)
\]
\[
V = 87.5\pi
\]
Now, using \( \pi \approx 3.14 \):
\[
V \approx 87.5 \times 3.14 \approx 274.375 \text{ cubic feet}
\]
Thus, the hot tub can hold approximately **274.375 cubic feet** of water.