Question

A square lawn has aroa 3200 ft^2. A sprinkler placed at the center of the lawn sprays water in a circular pattern as shown in the figure. What is the radius of the circle?The radius of the circle is ___ ft.(Simplify your answer. Use a comma to separate answers as needed.)

Answer 1

Answer: The radius of the circle is 40 ft.

Explanation

• The square lawn area is 3200 ft².

The formula for the area of a square (A) is:

$A=s^2$

where s represents the side.

If we replace the area, we can find the side:

$s^2=3200$

$\sqrt{s^2}=\sqrt{3200}$$s=40\sqrt{2}$

If the sprinkler is placed at the center of the lawn spraying water in a circular pattern that covers the lawn, the diameter ( d ) of the circle is equal to the diagonal of the square:

$d=\sqrt{s^2+s^2}$

Replacing the values:

$d=\sqrt{3200+3200}$

Simpifying:

$d=\sqrt{6400}$

$d=80ft$

However, as the radius ( r ) is half the diameter then:

$r=\frac{d}{2}$$r=\frac{80}{2}=40$

The radius is 40ft.