Calculate the Face Diagonal of a 3-Centimeter Cube: Finding Corner-to-Corner Distance

Given below is a cube that has edges measuring 3 cm.

What is the length of the diagonal of the face?

333

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Step-by-step video solution

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00:00 Find the length of the face diagonal in a cube
00:03 The edge length according to the given data
00:08 In a cube, all edges are equal
00:11 A face in a cube is a square, therefore all angles are right angles
00:14 Therefore, we'll use the Pythagorean theorem in triangle ABD
00:20 We'll substitute appropriate values according to the data and solve for DB
00:47 Extract the root
00:51 Factor 18 into 9 and 2
01:01 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Given below is a cube that has edges measuring 3 cm.

What is the length of the diagonal of the face?

333

2

Step-by-step solution

To find the length of the diagonal of a face of a cube with edges measuring 3 cm, we should consider the geometry of the face, which is a square.

The length of the diagonal d d of a square with side length s s is found using the Pythagorean theorem, which gives us:

Diagonal of the face=s2\text{Diagonal of the face} = s\sqrt{2}

Substituting the given value s=3 s = 3 cm, we have:

d=32d = 3\sqrt{2}

Therefore, the length of the diagonal of the face is 32 3\sqrt{2} .

3

Final Answer

32 3\sqrt{2}

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A cube has a total of 14 edges.

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