Calculus help?

Question

Let A be the area of a circle with radius r . If dr/dt= 3 , then when r=1, we have dA/dt=

Answer 1

Hey, just use the chain rule and it's really easy.
You want to find dA/dt, so write it out like this:

dA/dt = dA/dr x dr/dt

Notice that the "dr"s will cancel out and you're left with dA/dt
Also, remember you are already given dr/dt in the question.

Now, the question is, what's dA/dr. Looking at your variables, you know you'll need to pull out the "area of a circle" equation.

A = pi x r^2
dA/dr = 2 x pi x r

Beautiful. Now you're ready to solve dA/dt.

dA/dt = dA/dr x dr/dt
dA/dt = (2 x pi x r) x 3

Substitute r = 1 (coz the question told you to do so!)
dA/dt = 6 x pi

Answer 2

Think about the formulas you need to answer the question:
A = πr^2
That gives two variables, A and r.

Differentiate A = πr^2. Here's a start for you:
dA/dt = ....

Once you differentiate you can plug in the value for dr/dt as 3. There will also be an r value in the derivative, so plug that in last.

Answer 3

A = pi r^2
dA/dt = 2 pi r dr/dt = 2 pi (1) (3) = 6 pi

Answer 4

A = PI*r^2
dA/dt = dA/dr*dr/dt
dA/dt = 2PI*r*dr/dt
r=1 , dr/dt=3
dA/dt = 2*PI*1*3 = 6*PI

Answer 5

A=pir^2
dA/dt=dA/dr*(dr/dt)
dA/dr=2pir
=2pi*1
so dA/dt=2pi*3=6pi

Answer 6

A= pi * r^2
dr/dt=3
dA/dr=2pi*r
dA/dr * dr/dt = dA/dt = 6pi*r
r is evaluated at 1 so dA/dt=6pi

Answer 7

6π

A= πr²
dA/dr = π2r

dA/dt = dA/dr • dr/dt
π2r • 3
6πr
r=1
6π(1)
6π is the final answer!