Question

A packaging company needs to choose between two different cans for a new soup. The first can has a diameter of 3.25 inches and a height of 4.25 inches. The second can has a diameter of 4 inches and a height of 2.8 inches. The company wants to minimize the costs of producing the cans.What is the correct process for solving this problem?The company needs to compare the volume of each can. The volume of the first can is about 141 cubic inches, and the volume of the second can is also about 141 cubic inches. Since both cans have approximately the same volume, they will cost about the same for the company to produce.The company needs to compare the volume of each can. The volume of the first can is about 35 cubic inches, and the volume of the second can is also about 35 cubic inches. Since both cans have approximately the same volume, they will cost about the same for the company to produce.The company needs to compare the surface area of each can. The surface area of the first can is about 60 square inches, and the surface area of the second can is also about 60 square inches. Since both cans have approximately the same surface area, they will cost about the same for the company to produce.The company needs to compare the surface area of each can. The surface area of the first can is about 153 square inches, and the surface area of the second can is about 170 square inches. Since the first can has a smaller surface area, it will be less expensive for the company to produce.

Answer 1

So,

What we're going to do is to find the surface area of each can.

The formula to find the surface area of a can, is:

`2\pi r^2+2\pi rh`

For the first can, we know that:

`\begin{gathered} h=4.25in \\ r=1.625in \end{gathered}`

If we replace in the formula:

`\begin{gathered} S=2\pi(1.625in)^2+2\pi(1.625in)(4.25in) \\ S=59.98in^2\approx60in^2 \end{gathered}`

Now, we're going to find the surface area of the second can:

`\begin{gathered} h=2.8in \\ r=2in \end{gathered}`

Replacing:

`\begin{gathered} S=2\pi(2in)^2+2\pi(2in)(2.8in) \\ S=60.32in^2 \end{gathered}`

Therefore, the correct answer is C.

The company needs to compare the surface area of each can. The surface area of the first can is about 60 square inches, and the surface area of the second can is also about 60 square inches. Since both cans have approximately the same surface area, they will cost about the same for the company to produce.