Let A be the area of a circle with radius r . If d r d t = 3 , find d A d t when r = 5 .

Answer 1

A=pir^2

dA/dt = 2pi*r*dr/dt

dA/dt(5) = 2* pi * 5 * 3 = 30pi

Answer 2

A=pi(r^2)

if r=5

A = pi(5^2) = 25pi

=about 25(3.141593)

= about 78.54 = Area

or if, for some reason, you wanted to use calculus

find the area between the circle x^2 + y^2= 25 and the x axis

or find the area between the semi circle and the x axis

then multiply it by two

integrate to get the Area

dr/dt= r' = 5

A=pir^2

A' = 2pirr'

=2pi(3)(5) =30pi