The area of a circle increases at a uniform rate,then prove that the perimeter of the circle varies inversely with the radius.
pls show how to prove with steps!!
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Answers
Given : The area of a circle increases at a uniform rate
To Find : prove that the perimeter of the circle varies inversely with the radius.
Solution:
The area of a circle increases at a uniform rate
A = Area of circle
r = Radius of Circle
A = πr²
dA/dt = π2r.dr/dt
The area of a circle increases at a uniform rate = K constant
=> K = π2r.dr/dt
=> dr/dt = K/2πr
P= Perimeter of circle
P = 2πr
dP/dt = 2πdr/dt
Substitute dr/dt = K/2πr
=> dP/dt = 2π K/2πr
=> dP/dt = K/r
=> dP/dt ∝ 1/r
perimeter of the circle varies inversely with the radius.
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