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Question
Three cubes of sides x cm, 8cm and 10cm respectively are melted and formed into a single cube of edge 12cm, Find 'x'.
Solution
Given that:
Side (l1) of cube (a) = x cm
Side (l2) of cube (b) = 8 cm
Side (l3) of cube (c) = 10 cm
Edge length of new formed cube = 12cm
Volume of cube (a) = (l1)3 = x3 cm3
Volume of cube (b) = (l2)3 = 83 = 512 cm3
Volume of cube (c) = (l3)3 = 103 = 1000 cm3
Total Volume of all three cubes - Volume of 1 cube
x3 + 83 + 103 = 123
x3 + 512 + 1000 = 1728
x3 = 1728 - 1512
x = `root(3)(216)`
∴ x = 6cm.
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