Question 116

A colourless cube is painted blue and then cut parallel to sides to form two rectangular solids of equal volume. What percentage of surface area of each of new solids is not painted blue?

Solution

Assuming the sides of the cube = a, then surface painted blue = 6a$$^2$$

Now after cutting into half the blue surface = 3a$$^2$$ for each solid and a new colourless surface with area a$$^2$$ is generated.

Hence the total surface area = 3a$$^2$$ + a$$^2$$ = 4a$$^2$$

% surface area not painted blue = $$\ \dfrac{\ a^2}{4a^2}\times\ 100$$ = 25

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