If the Sum of the Lengths of the Edges of a Cube is 60

Question: If the sum of the lengths of the edges of a cube is 60, the volume of the cube is

1. 1,000
2. 422
3. 216
4. 150
5. 125

“ If the sum of the lengths of the edges of a cube is 60” –  is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "Official Guide for GMAT Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach 1:

Given:

• Sum of the lengths of the cube is 60

Find Out:

• The volume of the cube

We will take the image of the cube provided below:

Total Edges in a cube = 12 (refer the figure below)

If length of each edge = x then

i.e. Sum of lengths of all edges = 12*x = 60

i.e. x = 5

Volume of Cube = Side^3
i.e. Volume of cube = x^3
=>5^3
=>125

Approach 2:

Given:

• Sum of the lengths of the cube is 60

Find Out:

• The volume of the cube

We know that a cube has 12 edges.
The length of each edge of the cube is 60/12 = 5.
Thus, the volume of the cube is 5^3 = 125.

Approach 3:

Given:

• Sum of the lengths of the cube is 60

Find Out:

• The volume of the cube

We need to find the sides of the cube to get the volume.
Now, the problem statement says that the sum of lengths is 60.

Since this is one cube, the lengths of the sides will be same. As a cube has 12 sides, the length of sides will be 60/12 = 5.
Hence, volume is 5^3 = 125
Hence, E is the correct answer.

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