Question

Rachel sets up a sprinkler in her backyard for her kids to play in on a hot day. The water from the
sprinkler creates a circle that 70 ft is around the outside. What is the total area that the sprinkler
covers?

Answer 1

To find the area covered by the sprinkler, we need to use the formula for the area of a circle, which is:

\[
A = \pi r^2
\]

where \( r \) is the radius of the circle.

We know that the circumference (the distance around the circle) is 70 ft. The formula for the circumference of a circle is:

\[
C = 2\pi r
\]

We can set this equal to 70 ft to find the radius:

\[
2\pi r = 70
\]

To solve for \( r \), we divide both sides by \( 2\pi \):

\[
r = \frac{70}{2\pi} = \frac{35}{\pi}
\]

Now we can substitute \( r \) back into the area formula:

\[
A = \pi \left( \frac{35}{\pi} \right)^2
\]

Calculating \( r^2 \):

\[
\left( \frac{35}{\pi} \right)^2 = \frac{1225}{\pi^2}
\]

Now substituting that into the area formula:

\[
A = \pi \cdot \frac{1225}{\pi^2} = \frac{1225}{\pi}
\]

Now, using an approximation for \( \pi \) (approximately 3.14):

\[
A \approx \frac{1225}{3.14} \approx 390.78 \text{ square feet}
\]

Thus, the total area that the sprinkler covers is approximately **390.78 square feet**.