Question

Surface Area / Volume question.

Part 1: I need to create and provide the dimensions for two similar figures. (Rectangular Prisms) (Dimensions created below)
Part 2: I also need to provide what the similarity ratio of these figures along with the ratio of their surface area and volume are.
Part 3: Either using the actual volumes or using the formula, I need to show that the volume ratio is true.

Answer 1

My shape of choice: rectangle
dimensions L=2 W=3
similar rectangle is L=10 W=15

Answer 2

i think you need a 3 dimensional shape

Answer 3

So should I add height to the dimensions?

Answer 4

sure

Answer 5

Alright,
L=2 W=3 H=5
L=10 W=15 H=25

Answer 6

And we'll make it a rectangular prism i suppose.

Answer 7

^ precisely.

Answer 8

ok so what is total surface area of each

Answer 9

\[SA=2lb+2bh+2hl\]

Answer 10

and the volume is
\[V=lbh\]

Answer 11

Sorry just got back to my computer. Let me figure these out real quick.

Answer 12

SA1= 62
SA2= 1550

Answer 13

V1=30
V2=3750

Answer 14

So how does this look--


*1part:
rectangle 1- L=2, W=3, H=5
rectangle 2- L=10, W=15, H=25

*2part:
The ratio of these figures in similarity was 1:5
The SA to SA ratio was 1:25
The Volume to Volume ratio was 1:125
*3part:
Formula (Surface Area) SA=2lb+2bh+2hl
Formula (Volume)V=lwh
so
The first rectangle is 12+30+20={62(SA)}
Volume = 30
The second rectangle is 300+750+500={1550(SA)}
Volume = 3750
The second rectangle has area 25x the first rectangle
{the scale was 5, and the area scale is 5^2 (2x5=10, 3x5=15 etc.)}

Answer 15

ill change the rectangle -> rectangular prism but that was my template

Answer 16

looking great

Answer 17

Thanks for the help!

Answer 18

So the surface area of similar rectangular prisms has as ratio of the square of the similarity ratio.
And the ratio of their volumes is the third power of the similarity ratio.