Question

Some one please help me!
I need help with a question. I did the first two parts now I just need the last part.

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.
1. Rectangular prisms
Figure 1 - L:2 W: 3 H : 1
Figure 2 - L: 4 W: 6 H : 1

2. The similarity ratios is 1:2 because one figure 2 is twice as large as figure 1.

3.

Answer 1

shouldn't you also double H for Figure 2 (all dimensions are doubled or it won't be similar)

Answer 2

oh yes thank you I didnt see that

Answer 3

ok the height in figure 2 is 2 now

Answer 4

now i need to find a volume ratio?

Answer 5

Part 2: What is the similarity ratio of these figures along with the ratio of their surface area and volume?

I would tweak the answer to 2. they want the ratios of the surface area and the ratio of their volumes.

Answer 6

the volume is L*W*H
so for figure 1: volume is L*W*H
for figure 2: 2*L*2*W*2*H
the ratio of figure 2 to figure 1 is ?

Answer 7

Figure 1 = 6
Figure 2 = 48

Answer 8

and the ratio is ?

Answer 9

1:8?

Answer 10

6/48 is 1/8

or in general, if two similar figures (in 3D so they have volume), and they have a similarity ratio of k, the volume of the bigger figure will be k^3 (k cubed) bigger.

btw, when you say

The similarity ratios is 1:2 because one figure 2 is twice as large as figure 1.

I would change figure 2 is twice as large as figure 1.
because figure 2's volume is 8 times bigger than figure 1.

It is better to say that each dimension of figure 2 is twice as large as figure 1.

and surface area scales as k^2 (k squared)

so you should add to the answer for 2.
ratio of figure 2 area to figure 1 area is 2^2 =4
ratio of figure 2 volume to figure 1 volume is 2^3 =8

Answer 11

you just did 3.

or you could use the formula:

\[ \text{Volume ratio = }\frac{k*L*k*W*k*H}{L*W*H}= k*k*k= k^3 \]

Answer 12

wait whats the work for 3?

Answer 13

Part 3: Show your work, either using the actual volumes

that is what you did when you found 6 and 48
they want you to show that the volume ratio (big to small) is 2^3 = 8
and 48/6= 8

Answer 14

thank you