Question

Find the area of each sector.

Answer 1

D

Explanation:

You need to set up a ratio between the area of the sector & the area of the circle vs the angle of the sector & 360 degrees.

`(SectorAngle)/(360) =(SectorArea)/(CircleArea)`

That above is your formula you need to remember for these equations.

Now let's solve. You've been given the sector angle, which is 300 degrees, and you've been given the radius of the circle, 10 feet.

The area of a circle is the formula: A = πr²

Given that formula and you know the radius. You plug in 10 feet for r and solve for the area.

`A=\pi10^2\\A=314.159`

Now lets solve for the missing variable (Sector Area).

`(300)/(360) = (x)/(100\pi )\\100\pi * (300)/(360) = (x)/(314.159)*100\pi\\100\pi* (300)/(360) = x\\(250\pi )/(3) = x`

I kind of messed up since I didn't realize the answer choices were simplified, make sure for the area you don't completely solve the area, keep the pi simple if the answer choices include pi.

Answer 2

d. 250π/3

Explanation:

A = πr²

A = 3.14(10)² = 314.159

A = 314.159*(5/6) = 261.799

A = 261.799 = 250π/3