Find the volume of a cube if the sum of the lengths of its edges is 24 dm.
| March 12, 2021 | education
Since it is known that the sum of the lengths of all the edges of a cube is 24 dm, you can calculate the length of one edge.
Recall that all edges in a cube are equal, so you can count their number, after which the length of all edges is divided by their number.
The number of edges in any cube is 12.
24 dm / 12 = 2 dm.
It turns out that the length of the edge of the cube is 2 dm.
Now we find the volume of the cube using the formula V = a3. In our case, a = 2.
V = (2 dm) 3.
V = 8 dm3.
Thus, we found that the volume of a cube, the sum of the lengths of all edges of which is 24 dm, is 8 dm3.
Answer: the volume of the cube is 8 dm3.
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