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A cube has sides measuring 6 inches. What is the greatest

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A cube has sides measuring 6 inches. What is the greatest  [#permalink]

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New post Updated on: 21 May 2013, 01:15
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Question Stats:

33% (01:37) correct 67% (00:27) wrong based on 9 sessions

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A cube has sides measuring 6 inches. What is the greatest possible (straight line) distance, in inches, between any two points on the box?

Correct answer: 6\sqrt{}3


I read the explanation and understand that the greatest possible distance is from one opposite corner to the other (diagonal). I also understand how to find the diagonal of a face of the cube using the ratios of a 45-45-90 triangle. The diagonal is 6 sqrt of 2. This is where I get stuck. How do I use the diagonal of a face to come up with the diagonal of the entire cube?

Thanks!

Originally posted by josemnz83 on 20 May 2013, 14:51.
Last edited by Bunuel on 21 May 2013, 01:15, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Cube  [#permalink]

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New post 20 May 2013, 15:03
Look at the image.

You use Pythagora:\(6^2+(6\sqrt{2})^2\)
take the root
\(6\sqrt{3}\)

Let me know if it's clear
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Re: A cube has sides measuring 6 inches. What is the greatest  [#permalink]

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New post 21 May 2013, 01:18
josemnz83 wrote:
A cube has sides measuring 6 inches. What is the greatest possible (straight line) distance, in inches, between any two points on the box?

Correct answer: 6\sqrt{}3


I read the explanation and understand that the greatest possible distance is from one opposite corner to the other (diagonal). I also understand how to find the diagonal of a face of the cube using the ratios of a 45-45-90 triangle. The diagonal is 6 sqrt of 2. This is where I get stuck. How do I use the diagonal of a face to come up with the diagonal of the entire cube?

Thanks!


Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3 and 8. Thank you.

Similar questions to practice:
a-rectangular-box-is-10-inches-wide-10-inches-long-and-144733.html
a-rectangular-box-has-dimensions-of-8-feet-8-feet-and-z-128483.html
for-the-cube-shown-above-what-is-the-degree-measure-of-pqr-13841.html

Hope it helps.
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Re: A cube has sides measuring 6 inches. What is the greatest   [#permalink] 21 May 2013, 01:18
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