Question

A cuboid of dimension 60cm ×54cm×30cm. How many small cubes with 6cm can be placed in the given cuboid?

Answer 1

Hint: First, find the volume of the cuboid by the given length, breadth, and the height of the cuboid. After that find the volume of the cube by the given side of the cube. After that put these values in the formula to find the number of cubes to be filled inside the cuboid.

Complete step-by-step answer:
Given:- Length of the cuboid= l= 60 cm
Breadth of the cuboid= b= 54 cm
Height of the cuboid= h= 30 cm
Side of the cube= s= 6 cm
Let the number of the cubes be placed inside the cuboid be n, the volume of the cuboid be V and the volume of the cube be v.
Since, the cube is placed in the cuboid. So,
$n = \dfrac{V}{v}$.........…..(1)
Now, the volume of the cuboid is,
$V = l \times b \times h$
Put the values of the length, breadth, and height of the cuboid in the formula,
$\Rightarrow$$V = 60 \times 54 \times 30$
Multiply the values to get the volume of the cuboid,
$\Rightarrow$$V = 97200\,c{m^3}$
Now, the volume of the cube is,
$v = {s^3}$
Put the value of the side of the cube in the formula,
$\Rightarrow$$v = {6^3}$
Calculate the cube of 6 to get the volume of the cube,
$\Rightarrow$$v = 216\,c{m^3}$
Now, put the volume of the cuboid and the cube in equation (1),
$\Rightarrow$$n = \dfrac{{97200}}{{216}}$
Cancel out the common factors from both numerator and denominator,
$\Rightarrow$$n = 450$

Hence, the number of cubes that will be placed inside the cuboid is 450.

Note: Cube: A cube is a three-dimensional shape which is defined as an XYZ plane. It has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.
Cuboid: A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.