If the sum of the lengths of all the edges of a cube is 228 centimeters, find its volume.
Let’s begin by recalling how to find the volume of a cube. The volume is equal to 𝑒 multiplied by 𝑒 multiplied by 𝑒, or 𝑒 cubed, where 𝑒 represents the edge length of the cube. We haven’t been told the edge length of this cube directly, instead we’ve been told that the sum of the lengths of all the edges is 228 centimeters.
In order to calculate what the length of one edge is, we need to consider how many edges a cube has. There are four edges on the front face of the cube. There are another four edges on the back face of the cube. There four more edges connecting these two faces together, making a total of 12 edges overall.
Now that we know that the cube has 12 edges and they’re all of equal length, we can express this as an equation. As the sum of the lengths of all the edges is 228 centimeters, we have the equation 12𝑒 is equal to 228. To solve this equation, we need to divide both sides by 12, giving 𝑒 is equal to 19.
Therefore the edge length of the cube is 19 centimeters. Now let’s find its volume. The volume of the cube is equal to its edge length cubed, 19 cubed, which is 6859. The units for volume are cubic units, so we have that the volume of this cube is 6859 cubic centimeters.