Question

Related rates problem. Please check my work :)

Answer 1

Picture 1: original problem.

Answer 2

Sorry the first one is sideways! D:

Answer 3

how fast is the height of the water or cup rising?

Answer 4

cup can't be rising if it is constantly 12 cm high :p

Answer 5

I'm sure it is talking about the water

Answer 6

hahaha ik xD space alien cup!!

Answer 7

The prof makes typos ALL the time. So yeah I just went with the water.

Answer 8

why do you have a cube on h after taking derivative ?

Answer 9

eem because right above that we have
(h/3)^2 *h

Answer 10

I mean
v=(1/3)pi(h^2/9)*h so multiplying that h in. no?

Answer 11

OH lol i seee

Answer 12

\[\frac{dV}{dt}=\frac{pi}{27} \cdot 3h^2 \cdot \frac{dh}{dt}\]
should be that last line on that one page

Answer 13

bleh blonde moment.

Answer 14

so then it becomes 75 in place of 375 later

Answer 15

yeah
and you did good dV/dt=rate in-rate out

Answer 16

woop woop
so the answer comes out to
0.206 cm^3/sec

[that cm is meant to be cubed, right?]

Answer 17

cm shouldn't be cubed
height is not a 3 dimensional thing

Answer 18

how tall are you @Babynini something cm or something cm^3?

Answer 19

well....haha

Answer 20

okaaay :}

Answer 21

also.... you can plug the units in if you aren't sure...
\[V=\frac{1}{3} \pi (\frac{h}{3})^2 h \\ V=\pi \frac{h^3}{3^3} \\ V'=\pi \frac{3h^2}{3^3} h' \\ V'=\pi \frac{h^2}{3^2} h' \\ 1.8 frac{cm^3}{\sec}=\pi \frac{5^2 cm^2}{3^2} h' \\ \text{ solve for } h' \\ 1.8 \frac{cm^3}{\sec} \cdot \frac{3^2}{5^2 \pi \cdot cm^2}=h' \\ h'=\frac{1.8 \cdot cm \cdot 3^2}{ 5^2\pi \sec}\]

and rerange the units thing so it is a little more organized

Answer 22

like the units work just like numbers
they can be squared
they can cancel as in cm^3/cm^2 =cm^(3-2)=cm

Answer 23

like h was 5 cm
so h^2 was 5^2 cm^2

Answer 24

aah gotcha gotcha. yeah.

Answer 25

but yeah dh/dt should be a one dimensional unit over a time unit
because dh is about the height
and dt is about the time

Answer 26

so but erasing that ^3 on the cm at the end is all i have to fix, yeah? o.o

Answer 27

yeah

Answer 28

Thanks for explaining all that. it makes more sense now :}

Answer 29

Area is two dimensions
so if you see dA think a unit^2
where A represents area

Answer 30

volume is 3 dimensions
so dv would be unit^3

Answer 31

oh

Answer 32

ooh! I see!!

Answer 33

cool