Volume question?

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3 Answers
Feb 21, 2018

12cm

Explanation:

This is a generalisation of Pythagoras' theorem to 3 dimensions.

The length of the diagonal is:

sqrt(6^2+5^2+9^2) = sqrt(36+25+81) = sqrt(142) ~~ sqrt(144) = 12

Feb 21, 2018

The answer is 12 cm.

Explanation:

Firstly, you draw a diagonal line through the base of the rectangular prism. Now you get two triangles and can find the hypotenuse. 6^2 + 5^2 = 61^2

Now you can make a triangle and imagine that the diagonal line going through the whole prism is the hypotenuse and calculate it with the given height.

61^2 + 9^2 = 142^2

If you take the root out of 142 and turn it into decimal, you get 11.916...

Feb 22, 2018

12cm

Explanation:

Similar to the Pythagoras Theorem, the length of the diagonal for a rectangular prism is: sqrt(l^2+w^2+h^2)

Therefore, d=sqrt(6^2+5^2+9^2)

=>d=sqrt(36+25+81)

=>d=sqrt(142)

=>d~~11.92

12cm is the closest

The formula, by the way, can be used to find the diagonal of a similar situation in the 4D. (You just need to add another dimension squared)