Question

A large cube has a volume of 1 cubic unit. A small cube has a volume of 1 27 of a cubic unit. What is the difference between the edge length of the large cube and the edge length of the small cube?

Answer 1

Given:

Volume of Large cube = 1 cubic unit

Volume of small cube = $\dfrac{1}{27}$ cubic unit

To find:

The difference between the edge length of the large cube and the edge length of the small cube.

Solution:

Let the edges of large and small cubes are $a_1$ and $a_2$ respectively.

We know that, volume of a cube is

$V=(edge)^3$

Volume of Large cube = 1 cubic unit

$(a_1)^3=1$

Taking cube root on both sides, we get

$a_1=1$

So, edge of large cube is 1 unit.

Volume of small cube = $\dfrac{1}{27}$ cubic unit

$(a_2)^3=\dfrac{1}{27}$

Taking cube root on both sides, we get

$a_2=\dfrac{1}{3}$

So, edge of large cube is $\dfrac{1}{3}$ unit.

Now, difference between them is

$d=a_1-a-2$

$d=1-\dfrac{1}{3}$

$d=\dfrac{3-1}{3}$

$d=\dfrac{2}{3}$

Therefore, the difference between the edge length of the large cube and the edge length of the small cube is $\dfrac{2}{3}$ unit.