Question

What relationship does the volume of the dogs' pool have with the volume of the original family pool? How does this compare to the relationship in the dimensions of the dogs' pool to the dimensions of the family pool?

Answer 1

@Falco276

Answer 2

There are several versions of this questions with different dimensions that have been posted here before. I cannot open the document yet to see the pool dimensions on this problem.

Take a look at these discussions for guidance.

http://openstudy.com/updates/500886fee4b020a2b3bde878

http://openstudy.com/updates/50107ad1e4b009397c687e60

http://openstudy.com/updates/5008eeb0e4b020a2b3be40ef

@crystelle

Answer 3

im not really understanding how they explain this.

Answer 4

@Gin_Ichimaru @terryluce06 @So1D @Firejay5 @him1618

Answer 5

@Darrius @Directrix @wolfe8 @agent0smith

Answer 6

I'd recommend taking a screenshot... i prefer not downloading documents, uploaded screenshots are much easier.

Answer 7

idk how to screenshot but here is my workout @agent0smith
Family pool

1) Deep: 6 Wide: 20 Long: 20 Volume= 2400
2) Length x deep = 120 x 4 sides = 480. Bottom of pool 20 x 20 = 400. 480 + 400 = 880sqft
3)
• 6 - 0.5, = 5.5 .
• 5.5 x 20 x 20 = 2,200ft ^3
Dog pool
1) Deep: 1.5 Length: 5 Wide: 5 = volume of 37.5
2) 1.5 x 5(4) = 30. Bottom of pool: 5 x 5 = 25. 30 + 25 = 55 POOL LINING
3) 6-1.5 =1, 1 x 1.5 x 5 = 7.5 sqft of water.

Answer 8

@rrp240

Answer 9

@ganeshie8

Answer 10

@AravindG @ajprincess @april115

Answer 11

@dan815

Answer 12

@crystelle

The dog pool and the family pool are rectangular solds. They are similar as reflected in the ratio of the respective dimensions of depth, length, and width.

1.5 is to 6 as 5 is to 20 as 5 is to 20.

As an extended proportion:

6/1.5 = 20/5 = 20/5 which gives a scale factor of 1/4 or 1:4 from dog pool to family pool.

Answer 13

Recall this theorem:

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

That tells us that the ratio of the volume of the dog pool to the family pool is (1/4)³.

(1/4)³ = 1/ 64. That means that the family pool's volume is 64 times the dog pool's volume.

As according to your calculation, the family pool has volume 2400 and the dog pool, 37.5.

37.5/2400 = 1/64 as it should.

Answer 14

To answer this question:

What relationship does the volume of the dogs' pool have with the volume of the original family pool?

I don't know what the question author means by "relationship" as used in a mathematics problem but I will say what I would submit as an answer.

This is it:

As explained above, the volume of the dogs' pool is 1/64 the volume of the family pool.

Answer 15

How does ***this*** compare to the relationship in the dimensions of the dogs' pool to the dimensions of the family pool?

To answer this, read the theorem posted regarding the ratio of sides of similar solids.

Then, note that the second question asks about THIS which I assume refers to the 1/64 ratio of the volumes of the dog pool to the family pool.

The ratio of the dimensions of the dog pool to the family pool is 1/4 as explained above. The dog pool dimensions are 1/4 those of the family pool. Or, it can be said that the family pool dimensions are 4 times the dimensions of the dog poo.

And, once again, the connection between the two pools' dimensions and the respective volumes is that the cube of the ratio of the dog pool dimensions to the respective family pool dimensions is equal to the ratio of the dog pool volume to the family pool volume.

Answer 16

@crystelle I see only two questions posted at the top of the thread.

I see your work in which you calculate the area of the dog pool liner and the family pool liner.

The question about the area of the pool liners is not posted.

Your results are correct for the areas.

Answer 17

Consider this theorem:

If two solids are similar, the square of the scale factor of the two solids is equal to the ratio of any two corresponding area measurements of the solids.

The similarity of the dog pool to the family pool has been established as has the scale factor of 1/4 from the dog pool to the family pool.

The theorem gives us the ratio of the dog pool liner to the family pool liner.

That is this --> (1/4)² = 1/16

Interpret that as meaning that the area of the dog pool liner is 1/16 the area of the family pool liner. Or, the area of the family pool liner is 16 times that of the dog pool liner. You work reflects that as the fraction 55/880 reduces to 1/16.

Answer 18

I don't know the quesion for part 3 so I cannot help with that until you post the question.

Answer 19

"Or, it can be said that the family pool dimensions are 4 times the dimensions of the dog poo."

Really big dog turd, or a really small pool?

Answer 20

Well this is what my teacher said to help better understand

Answer 21

Answer the reflection questions. For question #1, you have to talk about the relationship of the volumes without steps. You don't just say that the dimensions are 1/4 the size, that is already established in the requirements. Next, talk about how this compares to the relationship in the dimensions of the dogs’ pool to the dimensions of the family pool. So, you are expected to discuss how the "change in dimension" affects volume.

Answer 22

@directrix

Answer 23

So, you are expected to discuss how the "change in dimension" affects volume.
-----------------

To my thinking, that is what I discussed here:

Recall this theorem: If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes. That tells us that the ratio of the volume of the dog pool to the family pool is (1/4)³. (1/4)³ = 1/ 64. That means that the family pool's volume is 64 times the dog pool's volume.

@crystelle

Answer 24

@Directrix thanks so much. I do have the other questions I was just doing it one at a time cause im slow in math >.<

Answer 25

What is the difference in volume when the pool is filled to the top versus filled to 6 inches below the top?

Answer 26

@crystelle

Answer 27

alrighty!

Answer 28

The family pool has dimensions (see above)

Deep: 6 Wide: 20 Long: 20

Volume= 2400 cubic ft. totally filled
----------------

If the pool water is dropped 6" in height, then the new height of the water is 5.5 feet because 6" is half a foot.

One the document posted above, this calculation appears:
6 - 0.5, = 5.5

V = 5.5 x 20 x 20 = 2,200ft ^3 --> volume of family pool when water level is dropped 6"

So the last task is to this subtraction: 2400 cubic ft - 2200 cubic feet = ? @crystelle

Answer 29

You can also think about the amount of water removed as a rectangular solid of dimensions .5 foot by 20 feet by 20 feet. The product of those numbers should equal the same number you got above when you subtracted. Let me know how it goes, okay?

@crystelle

Answer 30

Ok my answer came out to 200 @directrix

Answer 31

Alrighty so I wrote down the explanation on my document. last question

Answer 32

Was the amount of pool liner material representative of the lateral or surface area of a rectangular prism? Why or why not?

Answer 33

200 cubic feet, yes.

Wow, this problem is never-ending.

Question:

Is the pool liner material on just the walls of the pool or is it on the walls AND the bottom of the pool? That is the key to the last question about lateral or surface area. So what is your thinking on that? @crystelle

Answer 34

Here is the tips my teacher gave me for that question @directrix

Answer 35

you are expected to show you know what lateral area includes and what surface area includes. You should talk about both AND then analyze which one does the pool liner fit. Tell me if it fits the surface area, lateral area, both, or neither.

Answer 36

@crystal1_1

You need to know the difference between the concepts of lateral area of a geometric solid:

Lateral area is defined as the sum of surface area in an object by excluding the base area of the object.


and Total Area (also known as Surface Area)

Total area is the sum of the surface area of all the faces of a solid.

Answer 37

Assuming that you are in a rectangular solid room now, think about yourself as being in the family pool and sitting at the bottom.

Then, look around to see 4 walls, a ceiling, and a floor. That is a total of 6 faces.

Think about the swimming pool analogy. Does the swimming pool have a ceiling?

@crystal1_1

Answer 38

No it does not lol @directrix

Answer 39

So, the swimming pool liner covers the 4 "walls" of the pool and then the bottom of the pool. So that area is the lateral area plus ONLY ONE of the bases. Therefore, the computation of the pool linear area is NOT the same as total area of the rectangular solid.

Also, the pool liner area is NOT the lateral area of the rectangular solid because the pool liner area includes ONE base. So, my thinking is that the pool linear calculation is not directly a good fit for either the lateral area formula for a rectangular solid or the total surface area.

I would go with this: Neither.

Cogitate on it and let me know what you think.

@crystelle

Answer 40

^medal-worthy use of cogitate.

Answer 41

@crystelle

This may be the last question in the series:

4. Imagine Mrs. Noether asked you to add steps to the family pool. How would adding steps affect the volume of the water? How would adding steps affect the amount of pool liner material needed? Explain why each change would take place.

Answer 42

Oh wait. Its gone because I submitted half of it for feedback lol @directrix

Answer 43

but yeah thats the last question

Answer 44

Heyy @directrix . Yes it was on here.. I was just wondering do u know why she thought my volume of water would be wrong for the dogs pool?