Question

# The company compares the ratios of surface area to volume for two more containers . One is a rectangular prism with a square base. The other is rectangular prism with a rectangular base. One side of the base is equal to the side length of first container. And the other side is twice as long. The Surface area of this second container is . The heights of two containers are equal. Which has the smaller surface area -to – Volume ratio?

Hint:

### Surface area of a rectangular prism:

Volume of a rectangular prism:

We are asked to find which prism has smaller area to volume ratio.

## The correct answer is: Comparing both the ratio’s we get: 2x + 2h/x h and (2x + 3h )/x h for the first and second prism respectively. Analyzing them, it is evident that the second prism has much more ratio.

### Step 1 of 3:

Let be the length of the square base. Let the height of the prism be . The first rectangular prism has a square base, so the width and length of the prism is same. Thus, Surface area of the first rectangular prism is;

The volume is:

The ratio of the surface area to volume is:

Step 2 of 3:

The second rectangular prism has a rectangular base, the length is twice the length of the square base, that is: . The height is same for the both.

So, the volume of the second prism is;

The surface area is given as:

Their ratio is:

Step 3 of 3:

Comparing both the ratio’s we get: for the first and second prism respectively.

Analyzing them, it is evident that the second prism has much more ratio.

Ratio between two values can be written as .

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