Question

In a circle, a 90° sector has area 36π square inches. What is the radius of the circle?
36 inches
18 inches
12 inches
6 inches

Answer 1

Can I help?

Answer 2

Yes, please

Answer 3

Can you help me solve that question?

Answer 4

Okay, so here is a circle:


Now here is a circle with a \(90^{\circ}\) sector:


How much of the circle does that \(90^{\circ}\) cover?

Answer 5

A fourth of that circle

Answer 6

Correct

Answer 7

1/4 also 25% as a percentage

Answer 8

Correct, so if we have the area of one-fourth of the circle, what should we do to get the area of the whole circle?

Answer 9

36 divided by 4 times 3.14?

Answer 10

Put it this way: If I have \(\dfrac{1}{4}\) of something, what do I need to multiply \(\dfrac{1}{4}\) by to get \(1\) ?

Answer 11

9 times 3.14?

Answer 12

Probably not 9 times 3.14, I don't understand.

Answer 13

\(\dfrac{1}{4} \times 4 = \) ?

Answer 14

Oh, 1/4*4=1

Answer 15

Exactly and they gave you one fourth the area of the circle.

Answer 16

Is it 36 divided by 4?

Answer 17

What operation did you just perform? Division or multiplication?

Answer 18

1/4*4=1 would be multiplication

Answer 19

Correct. You had one-fourth and you had to multiply by 4 to get 1.

Now you have one fourth of the area of a circle and you need to get the area of one whole circle. So the operation must remain consistent.

Answer 20

Do I multiple 1 by something?

Answer 21

When you had one-fourth, what did you multiply by to get one?

Answer 22

Do I multiply 4 by something?

Answer 23

Yes

Answer 24

Is it 4 times 3.14?

Answer 25

What was the given area?

Answer 26

\(36\pi\) right?

Answer 27

Do I multiply 4 by 36?

Answer 28

Yes, by \(36\pi\)

Answer 29

We figured out that the \(36\pi\) was one-fourth of the circle. In order to get the area of the whole circle, we multiply by four.

Answer 30

36 times 3.14 is 113.04?

Answer 31

4 times 113.04?

Answer 32

@Ultrilliam we need a calculator on here

Answer 33

Is it 4 times 113.04?

Answer 34

Fine, I'll get to work on one, it shouldn't be too difficult to add

Answer 35

Thank you

Answer 36

Yes Katy, but we need to write it as \(36 \times 4 \times \pi\)

Answer 37

Because we want to find the exact radius

Answer 38

Okay

Answer 39

What is \(36 \times 4\)?

Answer 40

452.16

Answer 41

36 times 4 is different

Answer 42

Because we don't need to multiply the 3.14 to find the radius

Answer 43

144

Answer 44

Except we have to write it as \(144\pi\)

Answer 45

144 times 3.14 is

Answer 46

But we're not done yet

Answer 47

What you don't understand is we don't need to multiply 144 by 3.14

Answer 48

in order to find the radius

Answer 49

What we have to do is find the square root of 144

Answer 50

452.16

Answer 51

No, we don't need to do that.

Answer 52

find the square root of 144

Answer 53

Oh

Answer 54

12

Answer 55

Finally. That is the radius of the circle.

Answer 56

It wasn't as difficult as you were making it.

Answer 57

You focused too much on multiplying by 3.14 when that step was not necessary to find the radius.

Answer 58

They gave us \(36\pi\) which is one fourth the area of the circle.

Answer 59

To find the area of the whole circle we multiply by four to get
\(144 \pi\) square inches.

Answer 60

I have 4 more questions that I will have to do later.

Answer 61

Then we must realize we need to re-write the expression in the form \(r^2 \pi\) since this is the same as \(\pi r^2\) which is the area of the circle formula.

Answer 62

So since \(144 = 12^2\) we know that the area of the circle can also be written as \(12^2 \pi\) and 12 is the radius in inches.