Question

A child is playing with building blocks, which are of the shape of cubes, has built a structure as shown in the figure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.
A) \[270c{m^3}\]
B) \[243c{m^3}\]
C) \[216c{m^3}\]
D) \[189c{m^3}\]

Answer 1

Hint: Here first we will find the volume of one cube and then in order to find the volume of the given structure, we need to multiply the number of cubes in the structure to the volume of one cube.
The volume of a cube with edge a is given by:-
\[volume = {a^3}\]

Complete step-by-step solution:
It is given that the length of the edge of each cube is 3 cm.
We know that,
The volume of a cube with edge a is given by:-
\[volume = {a^3}\]
Hence, the volume of each cube with edge length 3 cm is given by:-
$\Rightarrow$\[{\text{volume of one cube}} = {\left( 3 \right)^3}\]
Simplifying it we get:-
$\Rightarrow$\[{\text{volume of one cube}} = 27c{m^3}\]
Now the total number of cubes in the given structure are 10.
Also, the total volume of the structure is given by:-
$\Rightarrow$\[{\text{total volume}} = {\text{number of cubes}} \times {\text{volume of one cube}}\]
Hence putting in the respective values we get:-
$\Rightarrow$\[{\text{total volume}} = {\text{10}} \times {\text{27}}\]
Solving it further we get:-
$\Rightarrow$\[{\text{total volume}} = 270c{m^3}\]

Therefore, option A is the correct option.

Note: All the edges of a cube are equal.
A cube with 6 faces and 6 sides.
Diagonals of a cube are equal
Students should take a note that in such questions first we need to find the volume of one cube and then we will be able to find the volume of all cubes which is the volume of the structure.