Question

Type the correct answer in the box. Assume that I = 3.14, and round your answer to the nearest integer.

45 yards
35 yards
a= 2800
The figure shows an aerial view of a playground. If David runs around the field three times, he covers a distance of
yards.
​

Answer 1

`648\ yd`

Explanation:

step 1

Find the circumference of the complete circle

The circumference is equal to

`C=2\pi r`

we have

`r=35\ yd`

substitute

`C=2\pi(35)`

`C=70\pi\ yd`

step 2

Find the measure of the arc length for a central angle of 280 degrees

Remember that the circumference subtends a central angle of 360 degrees

so by proportion

`(70\pi)/(360)=(x)/(280)\\ \\x=280*(70\pi )/360\\ \\x=54.44\pi\ yd`

step 3

Find the perimeter of the playground

`P=54.44\pi+45=54.44*3.14+45=215.96\ yd`

Multiply by 3

`215.96*(3)=647.87\ yd`

Round to the nearest integer

`647.87=648\ yd`