Question

How many cubic feet are in a cubic yard?

Answer 1

Hint: We will first write 1 feet in terms of yards. Then, we will multiply “1 feet” three times and 1 feet in yards three times as well so that we have 1 cubic feet on the left hand side and cubic yard on right hand side.

Complete step by step solution:
We are given that we are required to find how many cubic feet are there in a cubic yard.
Now, we already know that 1 yard equals 3 feet.
Therefore, it means that 1 feet is equal to $\dfrac{1}{3}$ yard.
Now, it can be written as follows:-
$ \Rightarrow $ 1 feet = $\dfrac{1}{3}$ yard
Taking cube on both the sides of the above equation, we will then obtain the following equation with us:-
\[ \Rightarrow {\left( {1feet} \right)^3} = {\left( {\dfrac{1}{3}yard} \right)^3}\]
Simplifying it, we will then obtain the following equation with us:-
\[ \Rightarrow 1feet \times 1feet \times 1feet = \dfrac{1}{3}yard \times \dfrac{1}{3}yard \times \dfrac{1}{3}yard\]
Simplifying the above equation further, we will then obtain the following equation with us:-
\[ \Rightarrow \left( {1 \times 1 \times 1} \right)\] cubic feet = \[\left( {\dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3}} \right)\] cubic yards
Simplifying the multiplication inside the brackets, we will then obtain the following equation:-
\[ \Rightarrow \] 1 cubic feet = \[\dfrac{1}{{27}}\] cubic yards
Now, we will just multiply 27 on both the sides of the above equation, we will then obtain the following equation:-
\[ \Rightarrow \] 27 cubic feet = 1 cubic yard

Thus, 1 cubic yard contains 27 cubic feet.

Note: The students must notice that if we would tried to convert 1 cubic yard into cubic feet, then we would have multiplied 1 yard three times in the left hand side and multiply 3 feet three times in the right hand side, so that we eventually get the following expression:-
\[ \Rightarrow \] 1 cubic yard = 27 cubic feet
Doing this, we would have obtained the result directly.
The students must commit to the memory the facts given below:-
1. 1 yard = 3 feet
2. 1 feet = $\dfrac{1}{3}$ yard