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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Comments
It doesn't have to be a cube. Any linear increase of 50% (x1.5) will result in a 125% increase in area and a 237.5% increase in volume. Incidentally, that is why babies need to drink more often than adults. Their surface area to volume ratio is much higher!
I ignored the cube and just did a square.
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