Help!
A spherical balloon is to be deflated so that its radius decreases at a constant rate of 7 cm/min. At what rate must air be removed when the radius is 5 cm?

Air must be removed at cm^3/min.

Question

Help!
A spherical balloon is to be deflated so that its radius decreases at a constant rate of 7 cm/min. At what rate must air be removed when the radius is 5 cm?

Air must be removed at  cm^3/min.

anonymous · Answer

@AuroraB

anonymous · Answer

@amistre64 help

amistre64 · Answer

what formulas do you think we will need to work this with?

anonymous · Answer

cilinder?

anonymous · Answer

im sorry i just dont know

anonymous · Answer

like i was doing one then i did the derivative

amistre64 · Answer

the word cylindar is used nowhere in the problem ...  maybe try the formula for the volume of a shpere

anonymous · Answer

ohh ok

amistre64 · Answer

so, what is that formula?  we will need to do an implicit derivative on it and plug in the given information

anonymous · Answer

so from the that equation, whats the next step

amistre64 · Answer

take the implicit derivative and fill in the pertinent information

anonymous · Answer

but like how would the equation look with the numbers

anonymous · Answer

i can do the implicit derivative after that

amistre64 · Answer

i need you to type out the formula for the volume of a sphere ...

amistre64 · Answer

the numbers are after the implicit derivative is taken :)

anonymous · Answer

V= (4/3)pi r^3

amistre64 · Answer

good, now the derivative with respect to time is?

anonymous · Answer

you want me to take the derivative of that equation?

amistre64 · Answer

of course

amistre64 · Answer

the only way i know of to get a rate of change for volume is to take the derivative of volume ....

anonymous · Answer

4 pi r^2

anonymous · Answer

whats next

amistre64 · Answer

almost .... the chain rule applies since this is not a derivative with respect to the radius,  but with respect to time;  so an r' pops out

V = (4/3)pi r^3

V' = 4 pi r^2 r'

now, they give us r and r' stated in the problem, so we just fill them in to solve for V'

anonymous · Answer

so how does it look

amistre64 · Answer

how does what look?

anonymous · Answer

4pi(7^2)(5)

anonymous · Answer

like that?

amistre64 · Answer

the radius is given as:  r = 5

the rate of change of the radius is given as:  r' = 7

so you have placed them in the wrong spots is all

anonymous · Answer

and after that i will get the answer right?

amistre64 · Answer

yes :)

anonymous · Answer

and that will be in cm^3/min?

amistre64 · Answer

yes