Question

Find the rate of change of the area of a circle per second with respect to
its radius
r
when
r
= 5 cm.

Answer 1

@agent0smith @Noemi95 @Shannon20150 @91004775

Answer 2

take the formula for the area of a circle
you are trying to find dA/dr

Answer 3

\[A=\pi r^2\]\[\frac{ dA }{ dt }=2 \pi r \frac{ dr }{ dt }\]

Answer 4

Evaluate the derivative at r = 5. To find the the dA/dt however, we also need dr/dt, the rate at which the radius is changing.

Answer 5

Did they give a dr/dt...?

Answer 6

with respect to radius, not with respect to time

Answer 7

ok then

Answer 8

@Peter14 "Find the rate of change of the area of a circle per second with respect to
its radius"

The wording is kinda confusing, really...

Answer 9

Unless we just have to leave it in terms of dr/dt.

Answer 10

OOps lol. Sorry I thought it was with respect to time. So it actually becomes:\[\frac{ dA }{ dr }=2 \pi r\] So at r = 5, it becomes:\[\frac{ dA }{ dr }=10 \pi\]

Answer 11

And you need to include the units.

Answer 12

@genius12 that's what I meant about the misleading wording: "Find the rate of change of the area of a circle per second with respect to its radius"

Answer 13

Thanks Sir