Question

Im gonna be honest i need help with 3 questions. that i seriously dont know anything about.. im close to giving up on this...

Answer 1

1. The theme park company is building a scale model of the killer whale stadium main how 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?



2. Using the same information from #5, what percent of change occurred from the actual tank to the mock-up of the tank?


3. If you were to take a cross section parallel to the base of one of the holding tanks, how would you describe the shape?

Answer 2

@SilenTempest @jim_thompson5910 ive been suck on these questions for dayss. :/ -__-

Answer 3

think of a cube

imagine it is 6 by 6 by 6

what is the volume of this cube?

Answer 4

216 ?

Answer 5

yes

Answer 6

now divide each dimension by 6

6 by 6 by 6 ----> 1 by 1 by 1

Answer 7

the new volume is??

Answer 8

1 ?

Answer 9

so the old volume is 216, the new is 1

you divide the old volume by 216 to get the new volume

you'll find that this trick works for any type of cube

Answer 10

let's say in general, the side lengths are s

so the volume of the cube is s^3

if you divide each dimension by k, then the new volume of the smaller cube will be \[\Large \frac{s^3}{k^3}\]

Answer 11

and this idea applies to any 3D shapes (not just cubes)

Answer 12

ok this is all for 1 ? im ngl but im a bit lost, just a bit.

Answer 13

yeah this is going to help you with #1

Answer 14

do another example

let's say the cube now has sides that are 10 inches long (so s = 10)

the volume of this cube is ______

then divide each dimension by 5 (so k = 5)

the volume of the new smaller cube is ______

Answer 15

compare the new volume to the expression (s^3)/(k^3) when s = 10 and k = 5

Answer 16

1000 is the cubes volume (s= 10)

Answer 17

k = 125

Answer 18

1000/125 = 8 right? @jim_thompson5910

Answer 19

the new volume is 8 ?

Answer 20

@jim_thompson5910 ^.^ :o

Answer 21

that is correct

also notice how 10/5 = 2 and 2^3 = 8

so the new volume is 1/8 of the old volume

Answer 22

that's for the example though

Answer 23

yesssssss. :o
lets see if i understand so in Q 1 : "s" S =6 right ? and K = nothing. just 6^3 ?

Answer 24

s is unknown for #1

k = 6 because we're dividing each dimension by 6

Answer 25

so

old volume = s^3

new volume = (s^3)/(k^3) = (1/k^3)*s^3

notice how I pulled out the 1/k^3

Answer 26

new volume = (1/k^3)*s^3

new volume = (1/6^3)*s^3

new volume = (1/216)*s^3

so we see that the new volume is 1/216 of the old volume (basically it's 216 times smaller)

Answer 27

so its 216 times smaller ?
lmfaoo sorry i was copying that in my notebook

Answer 28

yes it is

Answer 29

if we divided everything by 4 instead, it would be 4^3 = 64 times smaller

Answer 30

is it still right though ?

Answer 31

yeah I was just bringing up another example

Answer 32

ohhh i see.

Answer 33

for #2 all i have to do is turn it into percentage and subtract :?

Answer 34

what was the volume from #5 ?

Answer 35

thats actually #1 i forgot to change it. its not #5

Answer 36

ok let's say we go from

old volume = 216
new volume = 1

what is the percent change?

Answer 37

99.537 --> 99.5 ?

Answer 38

that's correct

Answer 39

thats all for # 2 ? Whatt ?

Answer 40

yeah we have roughly a 99.5% reduction

Answer 41

im finally understanding now ! :D

Answer 42

I'm glad you are

Answer 43

For #3 and i promise i wont bother anymore, would it be a cube or a triangle or a sphere?

Answer 44

what 3D shape are the holding tanks again?

Answer 45

sphere?

Answer 46

they mention a base though, so that's a bit odd

Answer 47

yup..

Answer 48

well if it is a sphere, then yes, the cross section will be a circle

Answer 49

imagine the shadow of the sphere

Answer 50

but the base thing is throwing me off

Answer 51

me too...

Answer 52

thats why i thought of a sphere