Question 43

What is the sum of the total surface areas of all the cubes formed when a cuboid of size 5.2m $$\times$$ 13m $$\times$$ 39m is cut completely into the least possible number of cubes, all of which arg identical?

Solution

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HCF of sides of cuboid = 2.6

So, side of each cube = 2.6 m

Least number of cubes formed = $$\frac{5.2 * 13 * 39}{2.6 * 2.6 * 2.6} = 150$$

Total surface area of each = $$6 * 2.6^2 = 40.56 m^2$$

Sum of total surface area of all the cubes = 150 * 40.56 = 6084 $$m^2$$

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