Question

A giant pie is created in an attempt to break a world record for baking. The pie is shown below:

A circle is shown with a central angle marked 38 degrees and the diameter marked 20 feet.

What is the area of the slice of pie that was cut, rounded to the nearest hundredth?

22.08 ft2

13.19 ft2

33.14 ft2

28.97 ft2

Answer 1

@whpalmer4 help please?

Answer 2

Okay, so you have a circle that has a diameter of 20 feet. Can you find the area of that circle?

Answer 3

the area is 314 @whpalmer4

Answer 4

You don't need to tag me each time you respond — once I've responded once, I'll get a notification each time you post.

Yes, though I would keep it as \(100\pi\) for as long as possible.

Okay, now we know the area of the entire circle. Do you know how many degrees there are in a circle, to make a full revolution?

Answer 5

hahaha okay and yes 360

Answer 6

Okay, so we have the whole circle's area = \(100\pi\), covered by \(360^\circ\). The wedge representing the slice of pie covers \(38^\circ\). Doesn't it stand to reason that we'll have a proportional chunk of the area of the entire circle?

Answer 7

im not quite sure

Answer 8

Well, if the angle of the slice is \(360^\circ\), that covers the entire pie, right?

If the angle of the slice is \(180^\circ\), that covers half the pie, right?

\[\frac{360^\circ}{360^\circ} = 1\]\[\frac{180^\circ}{360^\circ} = \frac{1}{2}\]

We can just multiply the area of the pie by the fraction of the entire \(360^\circ\) our slice takes up to get the area of our slice.

Answer 9

Did you get an answer?

Answer 10

Actually, strictly speaking the answer choices don't contain the correct answer :-)

Answer 11

if you use enough digits of \(\pi\) when computing the result, the hundredths place is larger than that given in the "correct" answer here.

Answer 12

Your answer should be \[\frac{38}{360}*100\pi\] expressed as a decimal number.