anonymous
  • anonymous
A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3cm/min. At what rate is the volume of the snowball decreasing when the diameter is 14 cm? (Note the answer is a positive number)
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
is there an equation for the volume of a sphere?
anonymous
  • anonymous
no :(
amistre64
  • amistre64
... im pretty sure there is. spheres have been studied now for quite some time, and some ancient mathmatikers are bound to have come up with some sort of formula that tells them how to determine the volume of a sphere. If not, i know a way that we can become very very rich :)

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More answers

anonymous
  • anonymous
haha i meant there's none that came with the problem! Not that none exist :)
amistre64
  • amistre64
;) you hunt down a formula for it, and then we can see what can be done to find an answer to this question then
anonymous
  • anonymous
it says online that it is 4/3nr^3 so i'm not really sure what that means but thats what i got :) I hope it helps!
anonymous
  • anonymous
the n is a pi
amistre64
  • amistre64
thats the one i was thinking of to find out how fast the volume is changing, we need to take its derivative; and we are in luck that we only have 1 variable and a power rule to deal with \[V=\frac43\pi~r^3\]
anonymous
  • anonymous
ok sounds good but i have a class right now :( so I dont know how you wanna do this because I'll be in class untill 12 :(
amistre64
  • amistre64
as long as you know what the power rule for derivatives is, that would help out alot
anonymous
  • anonymous
ok the radius is half the diameter right?
amistre64
  • amistre64
correct
anonymous
  • anonymous
i can find the derivative pretty easily but i'm just unsure what the radius would be
anonymous
  • anonymous
ok let me get you the derivative real quick
anonymous
  • anonymous
the derivative is 4pir^2 so that would be 4pi(7^2) and that would give me 615.44 about
amistre64
  • amistre64
very good, but there is one other part that needs to be addressed; the chain rule pops out an r'
anonymous
  • anonymous
ok... im lost
amistre64
  • amistre64
since the radius is half the diamter; the rate of change of the radius is half the rate of change of the diamter so multiply that result by .3/2
anonymous
  • anonymous
so that is 923.16 or so?
amistre64
  • amistre64
\[\frac d{dt}(V=\frac43\pi~r^3)\] \[\frac {dV}{dt}=\frac43\pi~3r^2*\frac{dr}{dt}\]
amistre64
  • amistre64
4pi(7^2)*.3/2 = about 92.36
anonymous
  • anonymous
lol alright i calculated wrong and thanks a million!
amistre64
  • amistre64
with a little practice, these should make more sense :) good luck
anonymous
  • anonymous
thanks :) ill be posting 2 more on here because I completely suck at this so maybe if you're on later you can help me again :) You actually help you don't just say the answer I like that :) Thank you! I have class now so hopefully I'll talk to you later!

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