Question

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 9 cm.

Answer 1

V=\[\frac{4}{3} \pi \left(\frac{D}{2}\right)^3\]
\[V=\frac{D^3 \pi }{6}\]
\[\frac{\text{dV}}{\text{dt}}=\frac{3\pi }{6}D^2 \frac{\text{dD}}{\text{dt}}\]

\[\frac{\text{dv}}{\text{dt}}=\frac{\pi }{2}D^2 \frac{\text{dD}}{\text{dt}}\]
we know dD/dt is -0.4
D=9

So let's plug them in
\[\frac{\text{dv}}{\text{dt}}=\frac{\pi }{2}9^2 -.04\]=-5.08938

Answer 2

I appreciate the time you've taken to elaborately explain this, but are you sure about your answer?

Answer 3

I think so

Answer 4

It's telling me that it's incorrect, and I don't think my answer was anywhere near that either (though chances are that I'm doing it wrong since I'm here asking for help)

Answer 5

Do you have the answer?

Answer 6

I'm working on 8 similar problems simultaneously, so I can't remember which answer pertains to which problem :/

Answer 7

so, we have no way to verfiy what the answer is?

Answer 8

maybe it want exact answer?

Answer 9

we do, I plug it in to my retarded online thing and it tells me whether it's right or wrong.

Answer 10

Cause what i am thinking is, that the differntiation of the formula for the volume of a sphere might be wrong. I think it is something like this: \[dv/dt=3(4/3)\pi(d/2)^2\]

Answer 11

I fortgot to multplu the right hand side by *dd/dt

Answer 12

so something like this: dv/dt=4pi(d/2)^2*dd/dt, where dd/dt is the change in diamter

Answer 13

Then we substitue the know values into that equation

Answer 14

so we get, dv/dt=(4)(pi)(4.5)^2(0.4)

Answer 15

I found pretty much the same problem online, followed the same method and still couldn't get the answer. The first one is the exact same problem, yet apparently wrong answer.

http://answers.yahoo.com/question/index?qid=20101108131052AAi84k0
http://answers.yahoo.com/question/index?qid=20090225144157AA7JlEO

Answer 16

what program are you tyrp typing it in to check for the answer?

Answer 17

it's an online homework program which prompts me for my answer; it's called webwork. Most of the errors are due to decimals, but not with these.

Answer 18

Is the answer 50.893 or 101.787

Answer 19

the first, omg! how did you get it?

Answer 20

I am a beast man, what can i say

Answer 21

lol just kiddin

Answer 22

Okay well here it is, the first guy that answered differentiatied the volume of the sphere wrong.

Answer 23

The volume of the sphere should diffentiate to : dv/dt=4*pi*(d/2)^2*dd/dt

Answer 24

I was wondering why that was chosen as best answer...

Answer 25

Now, you see where i have d/2, that is basically saying or means radius. But now since i have chosen to work with the radius, i have cut vaulue given in the problem in half, that is to say that i want to work with 0.2 not 0.4( for dd.dt or the rate at which the diameter is decreasing). So i simply susbtitute my numbers into the deferentiatied eqaution.

Answer 26

Then after multiplying things out we get: dv/dt=(4)(pi)(20.25)(0.2)=50.893

Answer 27

lol, I see. Thanks man

Answer 28

no prob.

Answer 29

My differentiation was right but I plug in wrong number
dD/dt=.4
D=9\[\frac{\pi }{2}9^2 (.4)\]
=50.8938