EXAMPLE 4 Solve a multi-step problem

A softball field forms a sector with the dimensions shown. Find the length of the outfield fence and the area of the field.

Softball

EXAMPLE 4 Solve a multi-step problem

SOLUTION

STEP 1

Convert the measure of the central angle to radians.

90º = 90º ( π radians180º ) =

π2

radians

EXAMPLE 4 Solve a multi-step problem

STEP 2

Find the arc length and the area of the sector.

πArc length: s = r = 180 = 90π ≈ 283 feetθ2

( )

Area: A = r2θ = (180)2 = 8100π ≈

25,400 ft2

π2

( )12

12

The length of the outfield fence is about 283 feet. The area of the field is about 25,400 square feet.

ANSWER

GUIDED PRACTICE for Example 4

9. What If? In Example 4, estimate the length of the outfield fence and the area of the field if the outfield fence is 220 feet from home plate.

The length of the outfield fence is about 346 feet. The area of the field is about 38,013 square feet.

ANSWER