Question

Volume question?

Answer 1

`12`cm

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`

Answer 2

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...

Answer 3

`12` `cm`

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)