Question

Consider a spherical cow that is consuming a great deal of hay. He is fattening himself up at a rate of 200 liters/day, so how quickly is her radius growing (in cm/da) when he can't fit through the circular stall door (that's 2 meters wide)?

Answer 1

@zimmah

Answer 2

So you know to use the volume of a sphere?

Answer 3

Ya, that's what we covered

Answer 4

So you are talking about rates, so differentiate the volume equation.

Answer 5

let me pull it up one sec

Answer 6

4/3*pi*r^3 right?

Answer 7

right, since we are talking about rates you will need to differentiate that

Answer 8

one sec i will

Answer 9

4(pi)(r)^3/3 right?

Answer 10

No do you know how to find derivative of r^3?

Answer 11

oh r^3 ok one sec

Answer 12

3r^2

Answer 13

ok so the 3 on top cancels the 3 on bottom

Answer 14

\[V'=\frac{4}{3} \pi (3 r^2) r' =4 \pi r^2 r'\]

Answer 15

but don't forget the derivative or r is actually r'
since r is a function of time

Answer 16

V' and r are given to you in your problem. Plug those in and solve for r'

Answer 17

find the derivative of 4pir^2?

Answer 18

No ...I'm asking you to plug in the numbers that were given to you.

Answer 19

at what rate was the volume changing?

Answer 20

200 liters/day i think

Answer 21

Replace V' with that.

Answer 22

Ah, yes, the infamous spherical cow, found in jokes such as this one:

Milk production at a dairy farm was low, so the farmer wrote to the local university, asking for help from academia. A multidisciplinary team of professors was assembled, headed by a theoretical physicist, and two weeks of intensive on-site investigation took place. The scholars then returned to the university, notebooks crammed with data, where the task of writing the report was left to the team leader. Shortly thereafter the physicist returned to the farm, saying to the farmer "I have the solution, but it only works in the case of spherical cows in a vacuum."

Answer 23

and what is the diameter?
Divide that by 2 to find the radius

Answer 24

What would the diameter be. imma little lost now