CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for The Diameter of a Circle is Increasing at the Rate of 1 Cm/Sec. When Its Radius is π, the Rate of Increase of Its Area is (A) π Cm2/Sec - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

The diameter of a circle is increasing at the rate of 1 cm/sec. When its radius is π, the rate of increase of its area is
(a) π cm2/sec
(b) 2π cm2/sec
(c) π2 cm2/sec
(d) 2π2 cm2/sec2

Solution

(c) π2 cm2/sec

\[\text { LetDbe the diameter andAbe the area of the circle at any timet. Then },\]

\[A = \pi r^2 \left( \text { where r is the radius of the cicle } \right)\]

\[ \Rightarrow A=\pi\frac{D^2}{4}\left[ \because r = \frac{D}{2} \right]\]

\[ \Rightarrow \frac{dA}{dt} = 2\pi\frac{D}{4}\frac{dD}{dt}\]

\[ \Rightarrow \frac{dA}{dt} = \frac{\pi}{2} \times 2\pi \times 1 \left[ \because \frac{dD}{dt} = 1 cm/\sec \right]\]

\[ \Rightarrow \frac{dA}{dt} = \pi^2 {cm}^2 /\sec\]

  Is there an error in this question or solution?

APPEARS IN

Solution for question: The Diameter of a Circle is Increasing at the Rate of 1 Cm/Sec. When Its Radius is π, the Rate of Increase of Its Area is (A) π Cm2/Sec concept: Rate of Change of Bodies Or Quantities. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
S
View in app×