The Well-Balanced Cube

Geometry Level 1

The volume of a cube with positive side length is numerically equal to the surface area of a cube (though they will have different units). What is the volume of the cube?

The answer is 216.

1 solution

Arron Kau Staff
May 13, 2014

Let $L>0$ be the side length of the cube. Then, the volume of the cube is $L^3$ and the surface area of the cube is $6L^2$ . Hence, we have $L^3 = 6L^2$ , which gives $0 = L^3 - 6L^2 = L^2(L-6)$ . Since $L>0$ , we get $L=6$ . Thus, $L^3=216$ is the volume of the cube.

The Well-Balanced Cube

The answer is 216.

1 solution

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