Question

The radius of a disk grows at 2cm/s. Calculate the growth rate of the disks area when the radius mesures 7 cm. (Designate the area of the disk with A and the radius with r)

A) Find the relation between A and r

B) Find the derivative of this relation on time t
dA/dt =

C) When r = 7cm and dr/dt = 2 cm/s, find dA/dt

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I'm just not sure for A, is the relation going to be dA/dt = dr/dA * dr/dt??

Answer 1

The area of the "disk" cannot be defined, because the height is missing. The area will be assumed to mean area of the circle.

A=πr²
dA/dt=<b>dA/dr</b>*dr/dt=2πr*2 cm²/s

Answer 2

A)A=Пr^2
B)dA/dt=dA/dr*dr/dt=2Пr*dr/dt
C)dA/dt=2П*7*2cm^2/s=87.96cm^2/s

Answer 3

All correct!

Answer 4

thank you!