To determine how much water the hot tub can hold, we need to calculate the volume of the cylindrical shape of the hot tub. The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height (or depth, in this case) of the cylinder,
- \( \pi \) is approximately 3.14159.
Given that the diameter of the hot tub is 10 feet, we can find the radius \( r \):
\[ r = \frac{diameter}{2} = \frac{10 \text{ feet}}{2} = 5 \text{ feet} \]
The depth \( h \) of the hot tub is given as 3.5 feet. Now, we can substitute the values into the volume formula.
\[ V = \pi (5 \text{ feet})^2 (3.5 \text{ feet}) \] \[ V = \pi (25 \text{ square feet}) (3.5 \text{ feet}) \] \[ V = \pi (87.5 \text{ cubic feet}) \]
Now, using \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 87.5 \approx 274.067 \text{ cubic feet} \]
Therefore, the hot tub can hold approximately 274.07 cubic feet of water.