Question

HELP ME PLEASE? dimensions

Part 1: Create and provide the dimensions for two similar figures of your choosing.
Part 2: What is the similarity ratio of these figures along with the ratio of their surface area and volume?
Part 3: Show your work, either using the actual volumes or using the formula, that the volume ratio is true.

Answer 1

To start this problem, you should first remember what "similar figures" means. Similar means that they have the same shape and angles, but the scale is different (i.e., one is proportionally larger to the other).

I would cubes or pyramids for this problem, but as an example I will use triangles or rectangles for simplicity. Rectangles might be slightly easier but triangles are good too.

Say we use rectangles. Make the sides of the first rectangle something easy to work with, maybe length 2 and width 3.
Next create a similar rectangle: Multiple each of the length and the width by some scale, or factor. You can use 2x, 3x, 5x, it doesn't matter.

Let's say we do 5x as our scale. Then the similar rectangle would have length 2*5=10, and the width would be 3*5=15. Do you see how the shapes are "similar" and differ only by their scale? You can do the same with 3-D shapes, and you would want to multiply the height by the same scale.

Next, you would compare their formulas for Surface Area and Volume.
Here I will show you the example with area, since my shapes do not have SA or Volume! :)

Our first rectangle (2x3) would have Area equal to A=b*h.
Our simliar rectangle (10x15) would have Area equal to A=5b*5h, or A=25*b*h.
This shows that there is a relationship between the first and second shapes with regard to their areas; the similar rectangle has area 25x the first rectangle, or a squared scale factor (the scale was 5, and the area scale is 5^2). We can also say that the ration of the first triangle to the second is 1/25 or the second to the first is 25/1, either way.

You would do similar for the formulas for volume and surface area of your 3-D shapes.

HTH! Good luck with your assignment!

Answer 2

Oh! Another good figure to use would be a sphere!

Answer 3

THANK YOU! :) It was very detailed.