A cuboidal storage box has length

MATHEMATICS · Subjective · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

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.

Related theory

Volume of Solids
Real Number System
Cube and cuboid volume
Mensuration

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