Question

A cuboid is reshaped into 3 cubes of equal volumes.
Volume (cuboid) = 3 x ______________
_____________ = 3 a3
If the dimensions of the cuboid are 27 m x 8 m x 3 m, then find the edge of the cube.

Answer 1

Dimensions of given cuboid = 27 m × 8 m × 3 m

We know that volume of a cuboid = lbh

= 27×8×3 m³ (no need to find it)

It is reshaped into three cubes of equal volumes.

Let edge of cube be 'a' metres

So volume of one of the cubes = a³ m³

Volume of three cubes = 3a³ m³

But total volume of cuboid = 3a³

So

$27\times8\times3 = 3a^3\\\\a^3 = 27\times8\\\\a = \sqrt[3]{27\times8}\\\\ a = 3\times2\\\\a = 6 \ \ m$

Edge of cube is 6 m