The radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

Solution

Let r cm be the radius of the circle.
From given condition, rate of increase = 3 cm per second
$therefore space space space space space space dr over dt space equals space 3$
Let A be the area of circle, $therefore space space space space straight A space equals space πr squared$
$therefore space space space space space rate space of space increase space of space area space space equals space dA over dt space equals space straight d over dt left parenthesis πr squared right parenthesis space equals space 2 space πr space dr over dt space space space space space space space space$
$equals space 2 πr cross times 3 space equals space 6 πr$ $open square brackets because space space of space left parenthesis 1 right parenthesis close square brackets$
When r = 10, rate of increase of area = $6 straight pi cross times 10 space equals space 60 straight pi space cm squared divided by sec$

For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

The radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

Some More Questions From Application of Derivatives Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction