Question

A container in the shape of this cuboid holds 2 litres of water.

Answer 1

Given:

Volume of cuboid container = 2 litres

The container has a square base.

Its height is double the length of each edge on its base.

To find:

The height of the container.

Solution:

We know that,

1 litre = 1000 cubic cm

2 litre = 2000 cubic cm

Let x be the length of each edge on its base. Then the height of the container is:

$h=2x$

The volume of a cuboid is:

$V=l\times w\times h$

Where, l is length, w is width and h is height.

Putting $V=2000,\ l=x,\ w=x,\ h=2x$, we get

$2000=x\times x\times 2x$

$2000=2x^3$

Divide both sides by 2.

$1000=x^3$

Taking cube root on both sides.

$\sqrt[3]{1000}=x$

$10=x$

Now, the height of the container is:

$h=2x$

$h=2(10)$

$h=20$

Therefore, the height of the container is 20 cm.