Question

5. Pop cans are often sold in boxes of 12 cans as shown. A can has a radius of approximately 3.2 cm and a height of approximately 12 cm. a) What is the volume of 12 pop cans? Volume b) What is the minimum volume of the box? Volume:

Answer 1

Explanation

Question A

We are told to find the volume of 12 pop cans

To do so, we will follow the steps below:

Step 1: List out the dimensions of 1 can

$\begin{gathered} \text{radius}=3.2cm \\ \text{height}=12cm \\ \end{gathered}$

Step 2: Find the volume of a can

$\begin{gathered} \text{Volume}=\pi r^2h \\ \text{Volume}=\pi\times3.2^2\times12 \\ \text{Volume}=386.04cm^3 \end{gathered}$

Step 3: Find the volume of 12 cans

$\begin{gathered} \text{Volume of 12 cans =volume of 1 can}\times12 \\ \text{Volume of 12 cans = 386.04}\times12 \\ \text{Volume of 12 cans}=4632.47cm^3 \end{gathered}$

Therefore, the volume of 12 pop cans will be 4632.47cm³

Question B

To get the minimum volume of the box, let us get the plan of the base of the box

Since the cans are arranged 3 x 4, then the dimensions will be

The base area of the box will be

$\text{Base area=length}\times Breadth=(3.2\times3)\times(3.2\times4)=122.88cm^2$

Then the minimum volume of the box will be

$\begin{gathered} Volume=\text{Base area}\times Height \\ \text{Volume}=122.88cm^2\times12cm \\ \text{Volume}=1474.56cm^3 \end{gathered}$

Thus, the minimum volume of the box will be 1474.56cm³