Question

1. Nancy is walking around a circular track with a radius of 45 feet. If she walks the equivalent of 210 degrees, find the total distance she has walked around the track to the nearest foot.

2. A windshield wiper blade is 18 inches long. Calculate the area covered by the blade as it rotates through an angle of 122 degrees. Round your answer ti the nearest square inch.

3. A spray irrigation system waters a section of a farmer's field. If the water shoots a distance of 75 feet, what is the area that is watered as the sprinkler rotates through an angle of 80 degrees? Round your answer to the nearest square foot.

Answer 1

see explanation

Explanation:

(1)

The distance walked ( arc length ) is calculated as

arc = circumference of circle × fraction of circle

= 2πr ×
`(210)/(360)`

= 2π × 45 ×
`(21)/(36)`

= 90π ×
`(7)/(12)`

≈ 165 ft ( to the nearest foot )

(2)

The area (A) covered is calculated as

A = area of circle × fraction of circle

= πr² ×
`(122)/(360)`

= π × 18² ×
`(61)/(180)`

= 324π ×
`(61)/(180)`

≈ 345 in² ( to the nearest square inch )

(3)

The area (A) is calculated as

A = area of circle × fraction of circle

= πr² ×
`(80)/(360)` ( r is the distance shot by sprinkler )

= π × 75² ×
`(8)/(36)`

= 5625π ×
`(2)/(9)`

≈ 3927 ft² ( to the nearest square foot )

Answer 2

9514 1404 393

Answer:

top down: 1, 5, 6, 4, 8, 2, 3, 7

Explanation:

It appears the expected order may be ...

__

Write the formula for the arc length of a circle with central angle, θ, in degrees.

\textit{Arc Length}=\dfrac{\theta}{360^{\circ}}\cdot 2\pi rArc Length=

360

∘

θ

⋅2πr

Replace 360° with 2π radians.

\dfrac{\theta}{360^{\circ}}=\dfrac{\theta}{2\pi}

360

∘

θ

=

2π

θ

Replace the angle ratio in degrees with the angle ratio in radians.

\textit{Arc Length}=\dfrac{\theta}{2\pi}\cdot 2\pi rArc Length=

2π

θ

⋅2πr

Simplify by cancelling

\textit{Arc Length}=\theta rArc Length=θr