IT ABOUT MEASURMENT

Question

Carla works at a container store. She is making plastic containers. She knows she uses 752 𝗰𝗺𝟮 of plastic for each container. The height of each container is 8 cm and the area of each base is 168 𝗰𝗺𝟮 . How can she determine the perimeter of the base?

 

 

SHOW Y'ALL WORK PLZ!!!

Answer 1

We have an unknown shape, so we don't know what the formula is for the Perimeter.

What if we divide the Surface Area (SA) by the Area of the base A_B?

SA / A_B = 752 / 168 = 4.476

Notice how the area of the base goes into the surface area more than 4 times but less than 5 times.

That tells us that the Base changes size as it projects up the height of the shape.

The base of the shape is a different size than the top of the shape.

If the Area of the base divides evenly into the surface area, then that would mean that the size of the base does not change as it projects up the height of the shape.

Calculus is normally required to solve problems where the cross-section of a shape changes as you travel up the height of a shape. However calculus can be avoided here if we assume that the cross-section changes size in a regular pattern. By regular pattern, we mean that the cross-sectional area may increase by 0.5 cm² for every two cm you travel up the shape. This is an example of a regular pattern. Not the actual pattern for this problem.

Making this assumption of a regular pattern, we may proceed with an algebraic solution.

Given any shape that has a consistent cross-section, throughout its entire height, the following relationship can be derived:

SA = ph + 2A_B

SA = Surface Area

p = perimeter of the cross-section

h = height of the shape

A_B = Area of the cross-section

In the calculation above, SA / A_B = 4.476 ⇒ SA = 4.476A_B

(4.476A_B) = ph + 2A_B

2.476A_B = ph

I will stop here to allow you to compute the solution.

If you substitute 168 cm² for A_B and 8 cm for h, you should get approximately 52 cm after you round your answer.

Our problem does not have a consistent cross-section, but assuming that it changes in a regular way, we can use the ratio of the Surface Area to the Area of the base as a way to get the perimeter of the base.

Verify the solution:

Take the equation SA = ph + 2A_B and substitute a number from the problem for each variable.

You should get 752 = 752 (A true statement). As long as you get a true statement, you have proven that the solution is correct.