Question

HELP!! - The radius of a spherical balloon is increasing at a rate of 2cm per minute. how fast is the volume changing when the radius is 14 centimeters.
Note: The volume of a sphere is given by V= (4/3)(pi)(r)^3

Answer 1

volume is a function of radius, and radius is a function of time

Answer 2

ok, whats my next step

Answer 3

differentiate everything with respect to time

Answer 4

not sure what i differentiate

Answer 5

both sides of the equation

Answer 6

the right side differentiated with respect to t is (4)(pi)(r)^2(dr/dt)

Answer 7

can you figure out the left side?

Answer 8

V?
wouldnt it just be dx/dt?

Answer 9

dV/dt yeah

Answer 10

so dV/dt = (4)(pi)(r)^2(dr/dt)

Answer 11

you are given r

Answer 12

r for radius so 10

Answer 13

uhh the problem says 14cm according to what i'm reading at the top

Answer 14

yeah my bad 14

Answer 15

you are also given dr/dt = 2

Answer 16

so you can plug those into the equation we just differentiated

Answer 17

and solve for dV/dt

Answer 18

1568pi

Answer 19

and its correct.. thank you