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

Step-by-step 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*3.2^2*12 \\ \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}*12 \\ \text{Volume of 12 cans = 386.04}*12 \\ \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}* Breadth=(3.2*3)*(3.2*4)=122.88cm^2`

Then the minimum volume of the box will be

`\begin{gathered} Volume=\text{Base area}* Height \\ \text{Volume}=122.88cm^2*12cm \\ \text{Volume}=1474.56cm^3 \end{gathered}`

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