Question

A cuboid is of dimensions 72 cm x 66 cm x 56 cm. Find the total number of small cubes

Answer 1

Answer:

154 small cubes.

Step-by-step explanation:

We are given the dimensions of the cuboid as 72 cm × 66 cm × 56 cm.

So, length of the cuboid, l = 72 cm

Breadth of the cuboid, b = 66 cm

Height of the cuboid, h = 56 cm

Capacity of cuboid = l × b × h = 72 × 66 × 56 = 266112 cm³

Now, we have to find the number of small cubes of side 12 cm each that can be placed in the given cuboid.

Now, length of each side of each small cube, s = 12 cm

Volume of each small cube = s³ = (12)³ = 12 × 12 × 12 = 1728 cm³

For calculating the number of small cubes that can be placed in the given cuboid, we will divide the capacity of given cuboid by volume of each small cube.

Required number of cubes = $\frac{Capacity\; of\; cuboid}{volume\; of\; each\; small\; cube}$

⇒ Number of cubes = $\frac{266112}{1728}=154$

∴ 154 small cubes each of side 12 cm can be placed inside the given cuboid of dimensions 72 cm × 66 cm × 56 cm.