Question 8

The sum of the lengths of the edges of a cube is equal to twice the perimeter of a square. If a quarter of the numerical value of the volumeofthe cube is equal to the numerical value of the area of the square, then the length of one side of the square is:

Solution

Let c be the length of the edge of cube and s be the length of side of square.

A/c to question ,

12c = 2 $$\times$$ 4s

3c = 2s

c = $$\frac{2}{3}s$$

Also ,

quarter of volume of cube = area of square

$$\frac{1}{4} c^3 = s^2$$

$$ \frac{8}{27 \times 4} s^3 = s^2$$

s =13.5

So , the answer would be option a)13.5 units.

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