Question

The sides of a square field are 28 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth. Use 3.14 for π.

Answer 1

168.24784 m²

Explanation:

Area of the square:

28 x 28=784 sq. m.

Area of the circle:

π(r²)=π(14)²=196π

=615.75216

Area not covered by the sprinkler:

784-615.75216=168.24784 m²

Answer 2

The sprinkler does not reach 168.56 m² of the field.

Explanation:

Find the circular area sprayed by the sprinkler.

A = πr² Use the formula.

A = π(14)² Substitute. Use 14 for r.

A ≈ 3.14 × 14² Substitute. Use 3.14 for π.

A ≈ 3.14 × 196 Evaluate the power.

A ≈ 615.44 Multiply.

The area of the circular area is about 615.44 ft².

Find the area of the square field.

A = s² Use the formula.

A = 28² Substitute. Use 28 for s.

A = 784 Evaluate the power.

The area of the square field is 784 m².

Find how much of the field is not reached by the sprinkler. Subtract the circular area sprayed by the sprinkler from the area of the square field.

784 − 615.44 = 168.56