### Brain Teasers

# Dimensional Increase of a Cube

If the length of each edge of a cube is increased by 50%, find the percentage increase in the cube's surface area.

### Answer

The percentage increase in the surface area of the cube = 125%.The surface area of a cube is (x^2 * 6), where x is the length of a side.

If you increase x by 50%, the new surface area is (1.5*x)^2 * 6. Divide the area of the new cube by the area of the original cube to get the ratio of the areas:

[(1.5*x)^2 * 6] / [x^2 * 6] = 1.5^2 = 2.25

(2.25 - 1) * 100% = 125% increase.

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