If the area of a circle increases at a u...

If the area of a circle increases at a uniform rate, then prove that the perimeter varies inversely as the radius.

Topper's Solved these Questions

APPLICATIONS OF DERIVATIVES
PRADEEP PUBLICATION|Exercise EXERCISE|502 Videos
APPLICATIONS OF INTEGRALS
PRADEEP PUBLICATION|Exercise EXERCISE|162 Videos

Similar Questions

Explore conceptually related problems

If the area of a circle increases uniformly, then show that the rate of increment of its circumference is inversely proportional to its radius.

If the radius of a circle is increasing at a uniform rate of 2 cm/s, then find the rate of increase of area of circt the instant when the radius is 20 cm.

Find the area of circle having radius 2 m

The volume of a cube is increasing at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side.

If the radius of a circle increases from 5 cm to 5.1 cm, find the increase in area.

If r be the radius of a circle. If the diameter is decreased by 1 unit, then what is the perimeter of the new circle formed?

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE

Find the rate of change of area of a square when its side is increasin...
Text Solution
|
If the rate of change of volume of a sphere is numerically equal to th...
Text Solution
|
If the area of a circle increases at a uniform rate, then prove that t...
Text Solution
|
Find a real number theta, 0 < theta < pi/2, which increases twice as f...
Text Solution
|
Find the rate of change of perimeter of a square when its side is incr...
Text Solution
|
Find the rate of change of perimeter of a square when its side is incr...
Text Solution
|
Find the rate of the change of surface area of a sphere when its radiu...
Text Solution
|
The volume of a cube is increasing at a constant rate. Prove that the ...
Text Solution
|
A particle is moving in a straight line such that its displacement s a...
Text Solution
|
The rate of change of the volume of a sphere w.r.t. its surface area, ...
Text Solution
|
Prove that the function f(x) = tanx-4x is strictly decreasing on (-pi/...
Text Solution
|
Find the interval in which the function f(X) = x^4 - (4x^3)/(3) is str...
Text Solution
|
Show that the function f given by f(x) = tan^-1(sinx+cosx), x>0 is alw...
Text Solution
|
State whether the function f(x) = x^3 is increasing or decreasing.
Text Solution
|
State whether the function f(x) = e^x is increasing or decreasing.
Text Solution
|
Is the function y = cot x decreasing on the interval (0,pi)?
Text Solution
|
Find the interval of increase of the function f(x) = tan^-1 x.
Text Solution
|
Find the interval of decrease of the function f(X) = sin x - 2x
Text Solution
|
Find the interval of increase of the function f(x) = 3x + cos x
Text Solution
|
Find the slope of the tangent to the curve y = 3x^2 at the point (1/6,...
Text Solution
|