Question

A spherical balloon has a circumference of 21 cm. What is the approximate surface area of the balloon to the nearest square centimeter?

A. 1,385 cm^2
B. 561 cm^2
C. 346 cm^2
D. 140 cm^2

Answer 1

What is the equation for the area of a sphere?

Answer 2

What do you mean?

Answer 3

Area \(A\) is given by \[A=4\pi r^2\]

Can you figure out the radius?

Answer 4

If I knew what the diameter was I could.

Answer 5

Or is there another way I could?

Answer 6

\(C=2\pi r^2\)

Answer 7

Right, I have the circumference which is 21. I'm trying to figure out the answer.

Answer 8

So given we have \(A=4\pi (\sqrt{\frac{C}{2\pi}})^2\)

Answer 9

Can you make this simpler for me please aha?

Answer 10

Use the Circumfrence formula to solve for r then plug that into the other one

Answer 11

\(C=2\pi r^2\) you are given \(C=21\) so we have \(21=2\pi r^2\) and we solve for \(r\) and we get \(r = \sqrt{\frac{21}{2\pi}}\)

Now we plug that into the Surface area formula I showed you the first time

\(A = 4\pi r^2 = 4\pi (\sqrt{\frac{21}{2\pi}})^2= 4\pi \frac{21}{2\pi}=42\)

Answer 12

So, basically my radius is 42?

Answer 13

no

Answer 14

I hate just asking for a straight out answer, but could you just give me the answer please?

Answer 15

I actually did. The fact that you dont know that is probably not a good thing...

Answer 16

Which part do you now understand about what I wrote?

Answer 17

now = not

Answer 18

Sorry zz but circumference is C = 2*pi*r no? :P

Answer 19

err yes

Answer 20

I'm confused because my brain is currently going crazy thinking about my grandfather who just passed away and the fact that I really wanna finish catching back up with school since I'm 56 lessons behind..

Answer 21

\(A = 4\pi r^2 = 4\pi (\frac{21}{2\pi})^2\)

Answer 22

OK Liv

We have \(C=2\pi r\)

and we are given circumference, so we have \(21 = 2\pi r\)

Are you with me so far?

Answer 23

Yes.

Answer 24

Ok so now we solve for \(r\) and get \(r=\frac{21}{2\pi}\)

Still with me?

Answer 25

Yeah, so 21/2*3.14?

Answer 26

that would be an approximate. But that part is not important right now. Just know \(r=\frac{21}{2\pi}\) ok?

Answer 27

Okay.

Answer 28

So now remember the Surface area of a sphere is \(A= 4 \pi r^2\) right?

Answer 29

Okay, that makes sense.

Answer 30

Before we didnt know \(r\) so we could not solve, but now we know what \(r\) is.

Answer 31

so plug in for \(r\) and we get \[A = 4 \pi (\frac{21}{2\pi})^2\]

Answer 32

That is the answer

Answer 33

So, it would be A?

Answer 34

Wow, wait I think I put the numbers in wrong..

Answer 35

what do you mean it would be A?

Answer 36

Yeah, I know I messed up.

Answer 37

The answer is \(4\pi (\frac{21}{2\pi})^2\approx 140.37\)

Answer 38

Ohhh. Wow.