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Find the length of the diagonal of a cube through side size of

.

You are watching: Length of a diagonal of a cube

Explanation:

, is the length throughout the cube native one vertex come the the contrary side"s vertex.

However, the cheat to solving the trouble is to additionally draw in the diagonal line of the bottom confront of the cube, which we labeled

.

Note that this create two appropriate triangles. Despite our finish goal is to find

, us can begin by looking at the ideal triangle in the bottom face to find

Now the we understand the value of

, we have the right to turn to our 2nd right triangle to find
using the Pythagorean Theorem.

Taking the square source of both sides and simplifying provides the answer.

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### Example question #2 : how To uncover The diagonal Of A Cube

What is the diagonal length for a cube v volume of

? round to the nearest hundredth.

Explanation:

Recall the the volume the a cube is computed utilizing the equation

, where
is the length of one next of the cube.

So, because that our data, we know:

Using her calculator, take the cube source of both sides. Girlfriend can always do this by raising

to the
power if her calculator does not have actually a varied-root button.

If girlfriend get

, the worth really must be rounded increase to
. This is because of calculator estimations. So, if the political parties are

, you can find the diagonal line by using a sport on the Pythagorean Theorem functioning for three dimensions:

This is

. Round it to
.

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### Example inquiry #3 : just how To discover The diagonal line Of A Cube

What is the size of the diagonal of a cube with a volume of

?

Explanation:

Recall that the diagonal line of a cube is most easily discovered when you recognize that cube"s dimensions. For the volume the a cube, the pertinent equation is:

, where
represents the length of one next of the cube. For our data, this gives us:

Now, you might factor this by hand or usage your calculator. You will check out that

is
.

Now, we uncover the diagonal line by using a three-dimensional variation of the Pythagorean organize / distance formula:

or

You can rewrite this:

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