Solved: The radius of a circle is increasing uniformly at the rate of \(3\;{\text{cm}}/{...

Q: The radius of a circle is increasing uniformly at the rate of \(3\;{\text{cm}}/{\text{s}}\). Find the rate at which the area of the circle is increasing when the radius is \(10\;{\text{cm}}/{\text{s}}\)

Explanation: We know that \(A = \pi {r^2}\) \[\therefore \dfrac{{dA}}{{dt}} = \dfrac{d}{{dr}}\left( {\pi {r^2}} \right)\dfrac{{dr}}{{dt}} = 2\pi r\dfrac{{dr}}{{dt}}\] Given that \(\dfrac{{dr}}{{dt}} = 3\;{\text{cm}}/{\text{s}}\) \[\therefore \dfrac{{dA}}{{dt}} = 2\pi r(3) = 6\pi r\] So, when \(r = 10\;{\text{cm}}\), \(\dfrac{{dA}}{{dt}} = 6\pi (10) = 60\pi {\text{c}}{{\text{m}}^2}/{\text{s}}\)

Class: 12 Subject: Math Topic: Application of Derivative

Question:

The radius of a circle is increasing uniformly at the rate of \(3\;{\text{cm}}/{\text{s}}\). Find the rate at which the area of the circle is increasing when the radius is \(10\;{\text{cm}}/{\text{s}}\)

Previous Question Next Question

QPaperGen

Question:

Solution