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 ${\displaystyle \frac{1}{3}}$ yard.
Now, it can be written as follows:-
$\Rightarrow$ 1 feet = ${\displaystyle \frac{1}{3}}$ yard
Taking cube on both the sides of the above equation, we will then obtain the following equation with us:-
$$\Rightarrow {\left(1feet\right)}^3={\left({\displaystyle \frac{1}{3}}yard\right)}^3$$
Simplifying it, we will then obtain the following equation with us:-
$$\Rightarrow 1feet\times 1feet\times 1feet={\displaystyle \frac{1}{3}}yard\times {\displaystyle \frac{1}{3}}yard\times {\displaystyle \frac{1}{3}}yard$$
Simplifying the above equation further, we will then obtain the following equation with us:-
$$\Rightarrow \left(1\times 1\times 1\right)$$ cubic feet = $$\left({\displaystyle \frac{1}{3}}\times {\displaystyle \frac{1}{3}}\times {\displaystyle \frac{1}{3}}\right)$$ cubic yards
Simplifying the multiplication inside the brackets, we will then obtain the following equation:-
$$\Rightarrow$$ 1 cubic feet = $${\displaystyle \frac{1}{27}}$$ 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 = ${\displaystyle \frac{1}{3}}$ yard