$A$ stone is dropped in a quiet lake and it is observed that waves move in circles. If the radius of a circular wave increases at the rate of $2 \text{ cm/sec}$, then the rate of increase in its area at the instant when its radius is $10 \text{ cm}$, is in $\text{cm}^2\text{/sec}$: (in $\pi$)
- A$40$
- B$80$
- C$10$
- D$20$
Explore More
Similar Questions
The surface area of a cube increases at a rate of $2 \ cm^2/sec$. The rate at which its volume increases when the length of its edge is $90 \ cm$ is ..... $cm^3/sec$.
Medium
View Solution$A$ particle moves in a straight line such that its displacement $S$ (in $m$) at a time $t$ (in $sec$) is given by $S(t) = t^3 - 4t^2 + 7t$. The instantaneous velocity $v$ at $t = 4$ is (in $m/sec$)
The sides of an equilateral triangle are increasing at the rate of $4 \text{ cm/sec}$. Find the rate at which its area is increasing when the side is $14 \text{ cm}$.
MediumKCET 2019
View Solution$A$ stone is dropped into a pond. Waves in the form of circles are generated and the radius of the outermost ripple increases at the rate of $5 \ cm/sec$. The rate at which the area increases after $2 \ seconds$ is:
The length of the side of a square sheet of metal is increasing at the rate of $4 \, cm/sec$. The rate at which the area of the sheet is increasing when the length of its side is $2 \, cm$,is ........ $cm^2/sec$.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo