Mathematics

Problem

A cuboidal storage box has length

2\sqrt{3}\,\text{cm}

, breadth

3\sqrt{2}\,\text{cm}

and height

4\sqrt{6}\,\text{cm}

. (a) Write an expression for the volume of the box in terms of these dimensions. (b) Simplify the expression obtained in part (a) to the form

k\sqrt{m}\,\text{cm}^{3}

, where

k

and

m

are positive integers and

m

is square-free. (c) If another box has dimensions exactly half of each corresponding edge of the first box, find and simplify the ratio of the volumes of the two boxes.

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