intermediary Geometry aid » heavy Geometry » Cubes » exactly how to find the length of an sheet of a cube

Given the the volume the a cube is , what is the size of any kind of one the its sides?    Explanation: The formula because that the volume is provided by Since we have actually the volume, we need to take the cube source of the volume to uncover the length of any type of one next (since it is a cube, all of the sides room equal).

You are watching: Can all edges have the same length? Plugging in 216 for the volume, we finish up with A challenge of a cube has a diagonal with a size of . What is the size of among the edges of the cube? Explanation:

Because this is a cube, it"s useful to remember the the value of the diagonal line of one face is the same size for the other 5 faces. Additionally, the size of one edge will be the same size of all the cube"s other edges. This helps relax the stress of there being more than one possible right answer.

To uncover the edge, we"re in search of the size of one of the sides of the square"s faces. The difficulty can be watched in a streamlined square convention:  The hypotenuse the the created triangle is , which deserve to be set equal come to deal with for , which in this situation will offer us the length of among the cube"s edges.   Therefore, the edge size of the cube is .

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### Example question #3 : Cubes

If the surface ar area the a cube is equal to , what is the size of among the cube"s sides? Explanation:

The surface ar area that a cube can be represented as , due to the fact that a cube has six sides and the surface area of every side is represented by its size multiplied by its width, which because that a cube is , since all of its edges are the same length.

We have the right to substitute into this equation and also then solve for :    So, one edge of this cube is in length.

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### Example inquiry #4 : Cubes

The volume that a cube is .

Find the size of the cube come the nearest tenth that a foot. Explanation:

Since the volume the a cube is length times broad times height, with every measurement being the same, we just need to take the cube source of the volume: .

Rounded to the nearest tenth, the length is 3.5 feet.

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### Example question #5 : Cubes

Find the size of among the cube"s sides: Cannot it is in determined Explanation:

The only information that is given is that the diagonal of one of the deals with of the cube is . Due to the fact that this is a cube, this is true because that the rest of the five faces. All the edges will additionally be the very same length, meaning this eliminates the opportunity of an ext than one exactly answer.

The edge of the cube deserve to be fixed for making use of the Pythagorean Theorem since the diagonal create two right triangles. Or, if you"re comfortable v it, you can remember that the diagonal creates 2 special ideal triangles that have their own rules through respect to fixing for sides.

Using the Pythagorean Theorem, , we deserve to simplify the equation follow to info we have and can deduce the exactly answer.

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The variables and refer to the foot of the best triangles. Since this is a cube, we deserve to deduce that the length of the legs will be the same. Therefore, . That way the Pythagorean to organize (for this case) can be rewritten as Looking back at the problem, the just information given is the hypotenuse for among the two triangles. This value deserve to be substituted in for . Then, as we resolve for , us will acquire the answer because that the question: the length of the edge.