Question

MODELING REAL LIFE A cereal box has a volume of 225 cubic inches. The length of the base is 9 inches and the width of the base is 2.5 inches. What is the height of the box? Justify your answer.

Answer 1

Hint: The cereal box can be considered as a rectangular prism. Use the formula of volume of rectangular prism in order to find the height of the cereal box.

Step 1: The volume $V$ of the prism is the product of the area of the base and the height of the prism. The cereal box is a rectangular prism in shape.

Given the volume$\left(V\right)$ is 225 cubic inches

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 cereal box & $w$ is the width of the cereal box.

Step 3: Here, The length (l) is 9 inches & the width (w) is 2.5 inches. Let’s suppose the height of the stack is h inches.

Let’s put all the values in the formula, we get

$$\begin{gathered} V=B·h \\ 225=(9\times 2.5)\times h \end{gathered}$$

In order to find the value of $h$, we need to simplify the equation,

$$\begin{gathered} 225=22.5h \\ 10=h \end{gathered}$$

Step 4: Justification: In order to justify we can simply find the volume of the stack with the given dimensions.

Here, The length (l) = 9 inches, width (w) = 2.5 inches, height (h) = 10 inches

$$\begin{gathered} V=B·h \\ =9(2.5)\times 10 \\ =22.5\times 10 \\ =225 \end{gathered}$$

Thus, The volume of the stack of paper is 225 cubic inches.

Final Answer: The height of the cereal box is 10 inches.