Question

The dimension of a cuboid are 25 cm, 20 cm and 16 cm.Find the length of a cube which has the same volume as this cuboid

Answer 1

volume of cuboid= 25×20×16=8000cm^3
a^3=8000
a=20cm
side of cube is 20 cm

Answer 2

ANSWER:

_____________________________

Given:


The length of the cuboid =25cm

The height of the cuboid =16cm

The breadth of the cuboid=20cm

We have the length, height and breadth of the dimensions of the cuboid so now we first need to find the volume of the cuboid so as mention it has the same volume as the volume of the cube but as we are not provided with the volume of neither the cuboid nor the cube.


So, Using the formula for volume of the cuboid we can easily find the volume.

$volume \: of \: the \: cuboid \: = l \times b \times h..........(length = 25cm \: breadth = 20cm \: height = 16cm \: all \: given \: in \: the \: question) \\ \\ volume \: of \: the \: cuboid = 25cm \times 20cm \times 16cm \\ \\ volume \: of \: the \: cuboid = 8000 {cm}^{3}$

We now have the volume of the cuboid =8000cm^3.

And as mention in the question,

Volume of cuboid =Volume of the cube i.e

$l \times b \times h = l ^{3}$



And now we are asked to find the length of the cube which has the same volume as that of the cuboid.

So,

$volume \: of \: cube = l ^{3} \\ \\ 8000 = l ^{3} \\ \\ l =2 \times 10......(factorizing \: 8000 \: in \: smaller \: numbers \: and \: thus \: taking \: the \: cube \: root \: ) \\ \\ l = 20cm$

Therefore,

Length of the cube with volume 8000cm^3=20cm