Question

A spherical balloon is inflated with gas at the rate of 800 cubic centimeter per minute. How fast is the radius of the balloon changing at the instant the radius is 30 centimeters?
V=4/3 pi (r)^3

Help,explain…please….cal help

Answer 1

Can you take derivative V'?

Answer 2

@jessiedeee Helo...0!

Answer 3

@Chlorophyll is it 4/3 ^2??

Answer 4

yes?? @Chlorophyll

Answer 5

No.o.0 !

Answer 6

well thats why I need help _-_

Answer 7

( r³)' = 3r² r'

Answer 8

dr/dt=800cm^3/min

Answer 9

-> V' =( 4π /3 ) 3r² r'
= ....

Answer 10

4pi/3 3r^3

Answer 11

No, ' 3 ' canceled out!

Answer 12

so it would be 4pi ®^2?

Answer 13

@Chlorophyll

Answer 14

-> V' =( 4π /3 ) 3r² r'
Don't forget r' :
-> V' = 4π r² r'
=> r' = ....

Answer 15

Then plug the numbers in to get the rate of change of radius with:
V' = - 800, r = 30 => r² = ...?

Answer 16

you lost me after r'…..

Answer 17

@Chlorophyll

Answer 18

The concept of related rate that you need to keep in mind is always take derivative with respect to time t => r'

Answer 19

ahh ok

Answer 20

thankyou @Chlorophyll

Answer 21

Then what's your r' result ?

Answer 22

0?
I didn't learn this

Answer 23

@Chlorophyll

Answer 24

This is just arithmetic, switching around to find r':
-> V' = 4π r² r'
=> r' = ....

Answer 25

4pi®^2