#### Ana.stasia

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- Thread starter Ana.stasia
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I would use the word "circumscribed" where you used both "described" and "inscribed", but I understand what you mean, I think.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 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.

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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.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.