# Prism and two balls HELP

#### Ana.stasia

##### New member
A regular three-sided prism is described around a ball, and a ball is inscribed around it. Determine the ratio of the area of the balls.

This is my work. Where did I go wrong?

#### Dr.Peterson

##### Elite Member
A regular three-sided prism is described around a ball, and a ball is inscribed around it. Determine the ratio of the area of the balls.

This is my work. Where did I go wrong?
I would use the word "circumscribed" where you used both "described" and "inscribed", but I understand what you mean, I think.

I used a much simpler method and got the same answer you did, 5:1. So maybe you are actually right. (I could be wrong, too!)

What I did was to take the radius of the inner ball as r, and think about a cross-section of the figure through the center of the ball and a vertical side of the prism. This led to finding that the radius of the outer ball is $$\displaystyle r\sqrt{5}$$, and therefore to your answer.

Make sure you looked at the answer to the right problem!

I can see a simple mistake they could have made to get an answer of 4:1. On the other hand, if the outer ball is not circumscribed about the prism (passing through all 6 of its vertices), but something else, then maybe we're solving the wrong problem.

#### Ana.stasia

##### New member
I would use the word "circumscribed" where you used both "described" and "inscribed", but I understand what you mean, I think.

I used a much simpler method and got the same answer you did, 5:1. So maybe you are actually right. (I could be wrong, too!)

What I did was to take the radius of the inner ball as r, and think about a cross-section of the figure through the center of the ball and a vertical side of the prism. This led to finding that the radius of the outer ball is $$\displaystyle r\sqrt{5}$$, and therefore to your answer.

Make sure you looked at the answer to the right problem!

I can see a simple mistake they could have made to get an answer of 4:1. On the other hand, if the outer ball is not circumscribed about the prism (passing through all 6 of its vertices), but something else, then maybe we're solving the wrong problem.
I believe the outer ball is circumscribed about the prism because those are the only types of problems we have been learning to solve. Thank you for your input.