Place the correct answer in each blank. Use pi = 3.14 and, if necessary, round your answers to the nearest hundredth.
The area of the largest cross section of a sphere and the circumference of the sphere are in the ratio 4 : 1.
The radius of the sphere is ______ cm. The circumference of the sphere is about ______cm. The area of the largest cross section is about ______cm^2. The volume of the sphere is about _____cm^3.

Question

Place the correct answer in each blank. Use pi = 3.14  and, if necessary, round your answers to the nearest hundredth.
The area of the largest cross section of a sphere and the circumference of the sphere are in the ratio 4 : 1.
The radius of the sphere is ______ cm. The circumference of the sphere is about ______cm. The area of the largest cross section is about ______cm^2. The volume of the sphere is about _____cm^3.

noseboy908 · Answer

I'm gonna have to mess with this one for a bit. I will return soon.

love_to_love_you · Answer

alrighty, thanks

noseboy908 · Answer

Are you given any other information?

love_to_love_you · Answer

Nope.

noseboy908 · Answer

I'm here, I just had to do a good deal of thinking. I think I have the solution, but It's gonna take a bit to explain.

love_to_love_you · Answer

Ahhh, I dont have much time. Okay lets try

noseboy908 · Answer

I'll do my best to make this swift. We know the two formulas for circumference and area of a circle are $$C = 2 \pi r$$ and $$A = \pi r^2$$

noseboy908 · Answer

And we know that the ratio given is 4:1, with C first and A second, so I restate the formulas as this: $$4(\pi r^2)=1(2 \pi r)$$

noseboy908 · Answer

Understand so far?

love_to_love_you · Answer

I think so yeah

noseboy908 · Answer

Ok, so I simplified the equation as follows: $$4(\pi r^2)=1(2 \pi r)$$ $$2(\pi r^2)=\pi r$$ $$2(r)=1$$ $$r= 1/2$$

noseboy908 · Answer

Do any of my steps confuse you?

love_to_love_you · Answer

No, I think I get it, I'm scrambling to get everything haha

noseboy908 · Answer

I know it's a lot, so I appreciate your patience. Now that we've established the radius, we can find every other value. Do you know the formulas for C, A, and V?

love_to_love_you · Answer

$$C = 2\pi \frac{ 1 }{ 2 }$$

love_to_love_you · Answer

A= $$\pi \frac{ 1 }{ 2 }^2$$

noseboy908 · Answer

You need not do the fancy formatting, so long as you can get the answers for me to confirm. :) Just try to solve the equations and give me your answers.

love_to_love_you · Answer

alright

love_to_love_you · Answer

V= 4/3 pi 1/2 ^2 ?

noseboy908 · Answer

The power on r should be 3, not two.

love_to_love_you · Answer

oops, sorry
V = 4/3 pi 1/2^3

noseboy908 · Answer

Yep, now solve. (Then state your answers for Area and circumference too)

love_to_love_you · Answer

C = pi  
A= 0.78539816 (calculator) 
V= 0.523759877

love_to_love_you · Answer

I'm probably wrong

noseboy908 · Answer

All your numbers agree with mine! Just one very important note: If this gets turned in on paper, it would be in your best interest to write down all the steps it took to solve this. An instructor can help you verify or otherwise answer this.

love_to_love_you · Answer

Alrighty, will do. Thank you

noseboy908 · Answer

Happy to help!

noseboy908 · Answer

If you have more time, then feel free to ask more.