Question

A spherical balloon is filled with helium at the rate of 8 in^3/sex . How fast is the diameter of the balloon increasing when the volume of the ballon is 36p in ^3?

Answer 1

id assume 4

Answer 2

how did you get that

Answer 3

relationship of 36 and 8

Answer 4

between*

Answer 5

4.5

Answer 6

you need to apply the chain rule of calculus

Answer 7

how

Answer 8

What is the expression for the volume of a sphere?

Answer 9

4/3 pie r

Answer 10

r 3d

Answer 11

r to the 3

Answer 12

4/3 pi r3

Answer 13

good, now express it in terms of the diameter instead of the radius

Answer 14

I am so confused

Answer 15

so 4/3 pi 2r3

Answer 16

because the diam is twice as large as radius

Answer 17

so the diameter is 4/3 pi 2r3

Answer 18

yea

Answer 19

V = 4/3*pi*r^3 but r=d/2
Now substitute and simplify

Answer 20

ok but how fast is the diameter of the balloon increasing when the volume of the ballon is 36pi

Answer 21

2/3

Answer 22

Can you solve for V in terms of d?