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.
-
Find the radius: The diameter of the hot tub is 10 feet, so the radius \( r \) is half of the diameter:
\[ r = \frac{10}{2} = 5 \text{ feet} \]
-
Determine the depth (height): The depth \( h \) of the hot tub is given as 3.5 feet.
-
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.