Question

Using tools How many cubic inches are in 1 cubic foot?

Use a sketch to explain your reasoning.

Answer 1

Hint: Imagine a cube of dimension $1ft$, its volume is going to be 1 cubic feet.

Step 1: The volume $V$ of the prism is the product of the area of the base and the height of the prism. Consider a cube of sides $1ft$.

Step 2: The formula of the volume of the prism is given by: $V=Bh$

Where $B$ is the area of the base & $h$ is the height of the cereal box.

Since, Area of the base $B=l\times w$

Where $l$ is the length of the cube & $w$ is the width of the cube.

Step 3: As shown in the picture the volume of the cube is 1 cubic foot.

Now look at the first dimension of the cube, We could fit 12 cubic inches side by side to equal the distance of 1 feet. Then if you take the width, We have to stack the 12 cubic inches side by side to equal the distance of 1 foot.

So, Just by looking at the bottom layer of the cube. We could figure out the area of the cube.

$$\begin{gathered} B=l\times w \\ B=12\times 12 \end{gathered}$$

Let’s check how many layers do we need to stack in order to get the height of the cube.

From the figure, we can determine the height (h) = 12 inches.

So, $V=B·h$

$$\begin{gathered} V=(12\times 12)\times 12 \\ V=1,728 \end{gathered}$$

Thus, 1 cubic feet is equal to 1,728 cubic inches.