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### Week 5 AMC10 Prep Course Homework

Week 5 AMC10 Prep Course Homework

A cube and a sphere share the same center. Each edge of the cube is half contained in the sphere. The ratio of the volume of the sphere to the cube can be written as Aπ:B for positive integer A and B with gcd(A,B)=1. What is A+B?

That is the question, I just need to know what it means by the edge of the cube is half contained in the sphere. Does it mean it is like inscribed or the sphere is bigger than it is? If you can, put a picture. That would help me a lot, thanks!

Re: Week 5 AMC10 Prep Course Homework

Sphere > Cube

Cube Edge:

__/____\__

^             ^

sphere intersections

Re: Week 5 AMC10 Prep Course Homework

Thanks!

Re: Week 5 AMC10 Prep Course Homework

I also need a bit of help understanding this problem. Is the problem saying that the corners of the cube touch the sphere?

Re: Week 5 AMC10 Prep Course Homework

Imagine this: You have a sphere

Ok good

(Don't actually)

You glue them onto the sphere, so then it looks like a Pac-Man came alive and was tired of eating hosts, so he decided to devour about half of a cube.

(Make sure that there is a bump on every "face" of the "cube" you just made, and the cross sections look like a circle with edges sticking out at 90 degree angles)

That's what this problem is describing.

Re: Week 5 AMC10 Prep Course Homework

And yes this is along the lines of what I actually picture in my head when I did this.

Re: Week 5 AMC10 Prep Course Homework

lol thanks!