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 answer

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.
  1. Determine the radius: Given the diameter of the hot tub is 10 feet, the radius \( r \) is half of the diameter:

\[ r = \frac{10}{2} = 5 \text{ feet} \]

  1. Use the depth: The depth \( h \) is given as 3.5 feet.

  2. 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:

\[ \boxed{274.38} \text{ cubic feet} \]