Question

need help with these questions. ill post my work.
3.Was the amount of pool liner material representative of the lateral or surface area of a rectangular prism? Why or why not?
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 1

Part 1:
1) The volume of the pool is given by V=lwd
Where l is length w is width and d is depth. You get to choose any volume between 1400 and 3200. Well I’ll go with V=3200 to make things easy
3200ft3 =lwd
Okay, so now choose a depth. So I choose the depth to be 8 feet. Now I have
3200ft3 =lw(8ft)
3200ft3 /8ft=400ft2 =lw

Now you can see why I chose those two numbers, you have a nice square there. so just make the length and width the same (l=w) and you can see that
L2 =400ft 2
l=20ft

So the final dimensions of the pool are 8 feet deep by 20 feet long by 20 feet wide.

2) Just calculate the surface area of the prism, but there’s no liner on the top, so subtract that amount(20ft∗20ft)+4(20ft∗8ft) =400ft 2 +640ft 2 =1040ft 2

3) If you drain 6" of water you are draining

v drained =dwl=0.5ft∗20ft∗20ft=200ft 3
and then just subtract this from the volume of the full pool
V required =3200ft 2 −200ft 3 =3000ft 3
you could also just do 7.5ft∗20ft∗20ft=3000ft 3

Part 2:
1) The volume of the pool is given by V=lwd
Where l is length w is width and d is depth. You get to choose any volume between 1400 and 3200. Well I’ll go with V=800 to make things easy
800ft3 =lwd

Okay, so now choose a depth. So I choose the depth to be 2 feet. Now I have
800ft3 =lw(2ft)
800ft3 /2ft=400ft2 =lw

Now you can see why I chose those two numbers, you have a nice square there. so just make the length and width the same (l=w) and you can see that
L2 =100ft 2
l=5ft

So the final dimensions of the pool are 2 feet deep by 5 feet long by 5 feet wide.

2) Just calculate the surface area of the prism, but there’s no liner on the top, so subtract that amount(5ft∗5ft)+4(5ft∗2ft) =100ft 2 +160ft 2 =260ft 2

3) If you drain 6" of water you are draining

v drained =dwl=0.5ft∗5ft∗5ft=50ft 3
and then just subtract this from the volume of the full pool
you could also just do 2.5ft∗5ft∗5ft=750ft 3
Questions:
1. 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?
o The dog pool is .25 the dimensions of the family pool.


2. What is the difference in volume when the pool is filled to the top versus filled to 6 inches below the top?
o You would have to factor in 0.5ft. You would subtract that.

Answer 2

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

Answer 3

I think you have to fix the 2nd part (the dog pool?)

because 5*5*2 does not equal 800

Answer 4

partner did part 2 so. idk I just need answers to questions 3&4 then I can turn this in

Answer 5

I would say surface area, as the liner includes the entire surface area minus the top side

if you build steps, they will take up some room, and so you will have less volume for the water

the front and tops of the stairs use the same surface area as the original wall and bottom

however, the sides take away surface area