The radius of a circle is increasing at the rate of 0.7 . What is the rate of increase of its circumference?

Let at any instant of time t , the radius of the circle be r and its circumference be C , then C = 2 r …(i) Differentiating (i) w.r.t. t , we get dt = 2 dt = 2 (0.7) = (1.4 ) Therefore the rate of increase of circumference = (1.4 )

Application of Derivatives — Class 12 Maths Solution

ncert exercise SA NCERT Ex.6.1,Q.No. 6,Page 198

Question

The radius of a circle is increasing at the rate of $0.7{\rm{cm/s}}$ . What is the rate of increase of its circumference?

Step-by-step Solution

Let at any instant of time $t$, the radius of the circle be $r$ and its circumference be $C$, then $C = 2\pi r$ …(i)

Differentiating (i) w.r.t. $t$, we get
$\cfrac{{dC}}{{dt}} = 2\pi \cfrac{{dr}}{{dt}} = 2\pi (0.7){\rm{cm/sec}}$
$= (1.4\pi ){\rm{cm/sec}}$

Therefore the rate of increase of circumference $= (1.4\pi ){\rm{cm/sec}}$

← All Application of Derivatives solutions Practice tests →

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Application of Derivatives. Curated by Sachin Sharma. Free for all students.