The internal measurements of a box are 10 cm long, 8 cm wide and 7 cm high. How many cubes of side 2 cm can be put into the box?

Since the height of the box is 7 cm, so only 3 cubes can be put height-wise. (If we put 4 cubes, the height becomes 8 cm which is more than the height of the box.)

Height of 3 cubes = 3 x 2 = 6 cm

∴ We will only consider height of box up to 6 cm for placing the cubes inside it.

By formula,

Volume of cuboidal box = l × b × h

Substituting values we get,

Volume of box = 10 cm × 8 cm × 6 cm = 480 cm³

By formula,

Volume of cube = (side)³

Substituting values we get,

Volume of cubes = 2 cm × 2 cm × 2 cm = 8 cm³

Let no. of cubes be n.

So, total volume of cubes = 8n cm³.

In order to fill the box with cubes,

Volume of cubes = Volume of box

∴ 8n = 480

⇒ n = $\dfrac{480}{8}$ = 60.

Hence, 60 cubes can be put into the box.