Question

The sides of a square field are 32 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

The sprinkler does not reach 220.16 m² of the field.

Explanation:

Find the circular area sprayed by the sprinkler.

A = πr² Use the formula.

A = π(16)² Substitute. Use 16 for r.

A ≈ 3.14 × 16² Substitute. Use 3.14 for π.

A ≈ 3.14 × 256 Evaluate the power.

A ≈ 803.84 Multiply.

The area of the circular area is about 803.84 ft².

Find the area of the square field.

A = s² Use the formula.

A = 322 Substitute. Use 32 for s.

A = 1,024 Evaluate the power.

The area of the square field is 1,024 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.

1,024 − 803.84 = 220.16

Answer 2

You find the area not touched by the sprinkler by subtracting the area of the circle from the area of the square. The area of the square is 32*32 which is 1024. The area of the circle is found by multiplying 3.14 by the radius squared. Our radius is half the diameter of 32, so r = 16. A=3.14(16)(16) which gives us an area of the circle to be 803.84. Subtracting the 2 areas, square minus circle, is 1024-803.84=220.16 meters squared.