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 total area that the sprinkler covers, we will use the formula for the area of a circle:

\[
A = \pi r^2
\]

where \( A \) is the area and \( r \) is the radius of the circle.

The problem states that the circumference of the circle is 70 ft. We can use the circumference formula to find the radius:

\[
C = 2 \pi r
\]

Setting \( C = 70 \):

\[
70 = 2 \pi r
\]

Now, solve for \( r \):

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

Next, we can substitute this value of \( r \) back into the area formula:

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

Calculating \( r^2 \):

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

Now substituting this into the area formula:

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

To find the total area, we can also calculate this numerically. Using the approximation \( \pi \approx 3.14159 \):

\[
A \approx \frac{1225}{3.14159} \approx 389.69 \text{ ft}^2
\]

Thus, the total area that the sprinkler covers is approximately:

\[
\boxed{389.69 \text{ ft}^2}
\]