Question 152

A rectangular box has dimensions x, y and z units, where x < y < z. If one dimension only is increased by one unit, then the increase in volume is

Solution

Let the dimensions of rectangular box beÂ $$3,4,5$$ units

=> Volume = $$V=3\times4\times5=60$$ cu units

Case 1Â : New length = $$4$$ units and breadth and height remains same

=> $$V'=4\times4\times5=80$$ cu units

Case 2 : New breadth = $$5$$ units and length and height remains same

=> $$V'=3\times5\times5=75$$ cu units

Case 3 : New height = $$6$$ units length and breadth remains same

=> $$V'=3\times4\times6=72$$ cu units

Clearly, increase in volume is greatest when $$x$$ is increased.

=> Ans - (A)

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