The sum of the lengths of all the edges of a cube is 6 cm. What is the volume, in cubic cm, of the cube?
A. [tex]$1 / 8$[/tex]
B. [tex]$1 / 4$[/tex]
C. [tex]$1 / 2$[/tex]
D. 1
Answer (2)
The sum of the lengths of all edges of the cube is 12 s = 6 cm.
Solve for the side length: s = 12 6 = 2 1 cm.
Calculate the volume using the formula V = s 3 = ( 2 1 ) 3 .
The volume of the cube is 8 1 cubic cm.
Explanation
Problem Analysis Let's analyze the problem. We are given that the sum of the lengths of all the edges of a cube is 6 cm. We need to find the volume of the cube in cubic cm.
Setting up the equation A cube has 12 edges, all of equal length. Let s be the length of one edge of the cube. The sum of the lengths of all edges is given by 12 s . We are given that 12 s = 6 cm.
Solving for the side length Now, we solve for s :
12 s = 6 s = 12 6 s = 2 1 cm So, the length of one edge of the cube is 2 1 cm.
Calculating the volume The volume V of a cube is given by the formula V = s 3 , where s is the side length. In our case, s = 2 1 cm. Therefore, the volume is: V = ( 2 1 ) 3 V = 2 1 × 2 1 × 2 1 V = 8 1 cubic cm
Final Answer The volume of the cube is 8 1 cubic cm.
Examples
Cubes are fundamental shapes in construction and design. For example, when designing a storage unit with cubic compartments, knowing how to calculate the volume based on the total edge length helps optimize material usage and space efficiency. If you know the total length of the material used for the edges, you can determine the size and storage capacity of each cubic compartment.
The volume of the cube, given that the sum of the lengths of its edges is 6 cm, is 8 1 cubic cm. This is determined by first finding the length of one edge to be 2 1 cm and then using the volume formula for a cube. Therefore, the answer is A.
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