Question

can you check if i made any mistakes?

Answer 1

5. The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up?

You can find the answer by dividing the old volume by the new volume. So first we find the new volume of the tank by taking its dimensions (it’s radius) and dividing it by six.
new radius = (old radius)/6
new radius = 70/6
new radius = 11.6666666667
And with the new radius, we can find the volume of the entire sphere…
V = 4/3 π r^3
V = 4/3 π 11.6666666667^3
V = 4/3π 158.96296297
V = 6482.06481484

Answer 2

@agent0smith

Answer 3

11^2 is 121, so there is no way 11^3 is 158. Reasonable estimation should tell you that it's way off.

Answer 4

Are you sure ? because when i put it in the calculator that's what it gave me

Answer 5

Again. Use reasonable estimations to check answers. What you wrote doesn't make sense. 11*11 is 121, so how can 11*11*11 be 158

Answer 6

see it's not 11 , its 11.6666666667 , i think that makes a difference

Answer 7

Well... that makes no sense, because 11.666 is bigger than 11. So 11.6666 cubed is bigger than 11 cubed...

Answer 8

well the reason i got that number is because i did > 70/6

Answer 9

What you seem to be saying is that because 11.666 is bigger than 11, then 11.666 cubed should be smaller than 11 cubed

Answer 10

should be bigger . 11^3 = 1331 , 11.666^3 = 1587.96296297

Answer 11

What you wrote above was not that number though.

Answer 12

yes it was , 11.6666666667 .

Answer 13

No... check your work on 11.666 cubed.

Answer 14

it's still the same ...

Answer 15

Go back and look at your working and you'll see it

Answer 16

Your original working.

Answer 17

70/6 = 11.6666666667 , i don't see why i would use 11.666 when that's not the full answer but let's say that i do 11.666^3 > 1578.6907563 . then ii would time it by 3.14 which gives me 4985.34897477 , then i would times it by the 4/3 >> 6480.9536672

Answer 18

You asked us to check your work. If you'll go back and check it, you will notice the mistake I am pointing out.

Answer 19

You made a typo. If you look at your original working you will see it

Answer 20

ooooh , it should be 1587.96296297

Answer 21

Finally lol

Answer 22

so the answer will be 6482.06481

Answer 23

Yeah looks about right. But keep in mind that isn't what the question asked for

Answer 24

_--_ it's not? wow , i am completely lost

Answer 25

Go back and read your first post, all the instructions are there

Answer 26

55.3846155131752423248504295 ?

Answer 27

is how many times smaller than the actual volume is the volume of the mock-up

Answer 28

how i got that was i took the volume of the actual tank and divided by the mock up tank .

the volume of the actual tank is 359006.6675

Answer 29

That's just a random number. And isn't correct. What is the volume of the big one??

If the radius is 6 times less, the volume should be 6^3 times less, so you know what you're looking for.

Answer 30

Wait, 55-point something is your final answer?

Answer 31

its not a random number, the volume of the big one is 359006.6675. the volume of the small one is 6482.06481481

Answer 32

and yes @mjdennis

Answer 33

Show work since your volume is wayyyyyy off

Answer 34

okay ,
V=4/3 (3.14)*(70)^3→ V=(1.3)*(3.14)*(343000)=1,400,126

Then I will have to divide the volume of the sphere by four
1,436,026.67/4= 359,006.6675.

this is how i received the big tanks volume. this part is correct according to my teacher.

so next i took the volume of the small tank , which we agreed was 6482.06481 and dived them together to receive 55.3846155131752423248504295 or just 55.

i didn't just pick any random numbers

Answer 35

Explain why you divided by four

Answer 36

i divided by four because the tank is a quarter-sphere sized tank

Answer 37

And explain why you did not divide the volume of the model by four?

Answer 38

Then why didn't you do that for the smaller tank?

Answer 39

It also would have been helpful had all the information been posted at the start. You never mentioned it was a quarter tank...

Answer 40

sorry , i didn't think i needed to divide by four .

opps , okay so if i divide the 6482.06481 by 4 it would give me 1620.5162025 .

Answer 41

then im guessing that i would take the 1620.5162025 and divide it by the 359006.6675? and this would give me my answer?

Answer 42

Yes. And the scale model would have to be a quarter tank too, or else... it's not a scale model, so yes you'd need to divide the spheres volume by 4

Answer 43

okay then my answer will be 221.5384622172575902

Answer 44

this means that the mock up tank is 221 times smaller then the actual tank

Answer 45

Much better

It would be exactly 6^3 like I mentioned earlier but that's probably fine

Answer 46

oo thank you , i understand this much better now.

Answer 47

It would be 6^3 since volume is a function of radius cubed, so if you decrease radius by a factor of 1/6, you decrease volume by a factor (1/6)^3

Answer 48

okay. i understand