Question

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

@amistre64 @ParthKohli

Answer 2

make 2 squares of different sizes and then apply the rest of the instructions ....

Answer 3

like.... 4in by 4in and 5in by 5in?

Answer 4

or 4by4 and 8by8? That might be easier for the similarity ratio, right?

Answer 5

yes, and to make it even simpler

4x4 and 12x12 that way one is a multiple of the other and you aint got to fight fractions

or yes, 4x4 and 8x8 :)

Answer 6

okay, so part 1 I just write 4by4 and 8by8, what about part 2 and 3 though?

Answer 7

its asking for volume and surface area, so lets just turn these into cubes

Answer 8

how?

Answer 9

umm, include a 3rd dimension?

4x4x4 and 8x8x8

Answer 10

surface area of a cube is the sum of the side areas: 6 sides of dimensions s*s

volume is side area * length; (s*s)*s

Answer 11

the ratio of sides is just comparing the lengths: 4:8 and reduce, 1:2

compare the surface areas and volumes in the same fashion

Answer 12

so, for part 1, its two cubes not squares?

Answer 13

correct, since a square has neither surface area (it has perimeter) nor volume (it has area)

Answer 14

whats their surface area? how do I find it?

Answer 15

@amistre64

Answer 16

i detailed that like 6 posts up

Answer 17

@amistre64 what do I multiply by 6? I don't get it.....

Answer 18

how do you find the area of a square?

Answer 19

the surface of a cube is made up of 6 equal squares; so the surface area is the sum of hte 6 areas

Answer 20

@amistre64 so its the area of the square times 6?

Answer 21

im wondering if there is somehting amiss with the internet connection ...

but yes, the area of the square times 6 will work fine

Answer 22

so, first surface area is 4*4*6, and the other is 8*8*6

Answer 23

using that as the similarity ration, and reducing we get

4.4.6:8.8.6

6:2.2.6

1 : 4

Answer 24

the volume of course is just the multiplication of length width and height

4.4.4 : 8.8.8

1 : 2.2.2

leaving us with a 1 : 8 ratio