Question

The radius of a spherical balloon is growing at the rate of 50 cm/s. How quickly is the volume increasing when the radius is 6 cm?

Answer 1

well you know these things

\[\frac{dr}{dt} = 50\]

you also know

\[V = \frac{4}{3} \pi r^3\]

so you then need to find the 1st derivative of volume with respect to the radius

\[\frac{dV}{dr}\]

to find the rate of change in volume with respect to time its

\[\frac{dV}{dt}= \frac{dV}{dr} \times \frac{dr}{dt}\]

the last task is to substitute r = 6 into dV/dt to find the answer.

Hope it helps

Answer 2

?

Answer 3

ok... so you haven't studied related rates..?

Answer 4

if you have studied calculus can you find the 1st derivative of the volume, with respect to r.

which means finding dV/dr

Answer 5

i dont get it.

Answer 6

so you don't get calculus... or related rates..?

Answer 7

you dont get, anything that campbell is saying? what course is this in?

Answer 8

we want how V chainges with respect to time, so i just do dV/dt implicitly and fill in the rest

Answer 9

i spose %50 is the same regardless of how you approach it :)

Answer 10

*50 ... my fingers hate me

Answer 11

will my answer be 245 pi?

Answer 12

no it's not

Answer 13

can I ask, do you know how to differentiate..?

Answer 14

yes,just confused with the porblem

Answer 15

ok... so make it smaller problems...

if

\[V = \frac{4}{3} \pi r^3\]

can you find

\[\frac{dV}{dr}\]

or the 1st derivative of the volume with respect to r... ?

Answer 16

so the value \[\frac{4}{3} \pi\] is a coefficient like 5 in 5x

so you are really just need to find the derivative of V = r^3

Answer 17

216?

Answer 18

no, that is just substituting r = 6....

the substitution is the last step

so I need you to do

\[If~~V = r^3~~~what~~is ~~~\frac{dV}{dr} = \]

Answer 19

Where did everybody go?

Answer 20

idk

Answer 21

so any thoughts on what the derivative would be..?

Answer 22

i was out sick for the class-so no not really

Answer 23

here is some information that may help you understand related rates

http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx

https://www.khanacademy.org/math/differential-calculus

the notes are worth reading, and the Khan academy stuff contains notes and hopefully some videos...

I think you need to understand differentiation before doing this question on related rates...

Its about have sound basics... to achieve success

Answer 24

what about this maths problem?

Answer 25

So I'll leave... I'm sure someone will provide you with an answer if the question is left open...

But I think you need to do some revision 1st

Answer 26

alright.

Answer 27

Well it appears that knowing how to differentiate is prerequisite for related rates.

Answer 28

If I differentiated for dV/dr do you think you could do the rest of the math?

Answer 29

I just checked out those links provided by campbell_st, they are really good, especially the second one. I believe after watching several videos you will have no problem solving this problem.

Answer 30

i will check it out.