To calculate the volume of water that the hot tub can hold, 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 (or depth) of the cylinder.
- Determine the radius: Given the diameter of the hot tub is 10 feet, the radius \( r \) is half of the diameter:
\[ r = \frac{10}{2} = 5 \text{ feet} \]
-
Use the depth: The depth \( h \) is given as 3.5 feet.
-
Plug in the values:
\[ V = \pi (5^2)(3.5) \]
Calculating \( 5^2 \):
\[ 5^2 = 25 \]
So the volume formula becomes:
\[ V = \pi \times 25 \times 3.5 \]
Multiplying \( 25 \) and \( 3.5 \):
\[ 25 \times 3.5 = 87.5 \]
Now we can complete the volume calculation:
\[ V = \pi \times 87.5 \]
Using \( \pi \approx 3.14 \):
\[ V \approx 3.14 \times 87.5 \approx 274.375 \text{ cubic feet} \]
Thus, the volume of water that the hot tub can hold is approximately:
\[ \boxed{274.38} \text{ cubic feet} \]