Question

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

The figure shows an aerial view of a playground. If David runs around the field three times, he covers a distance of (BLANK)
yards.

Answer 1

Length of an arc of a circle:
L = n° / 360° · 2 r · π = 280°/360° · 2 · 35 · 3.14 
L = 170.9 yards 
170.9 + 45 = 215.9 
3 · 215. 9 = 647.7 ≈ 648 
... he covers the distance of 648 yards.

Answer 2

Answer: 648 yards.

Step-by-step explanation:

Given: Central angle = 280°

Radius = 35 yards

The length of arc with central angle x and radius r is given by :-

$l=\dfrac{x}{360^{\circ}}\times2\pi r\\\\\Rightarrow\ l=\dfrac{280}{360}\times2\pi(35)\\\\\Rightarrow\ l=171.042266\approx171\text{ yards}$

Total distance = 171 +45 = 216 yards

Now, if David runs around the field three times, he covers a distance = $3\times216 =648\text{ yards.}$