The radius of a right circular cylinder incre | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $\frac{dr}{dt} = c$ and $h = ar + b$.Given $\frac{dh}{dt} = 3 \frac{dr}{dt}$,so $a \frac{dr}{dt} = 3 \frac{dr}{dt}$,which implies $a = 3$.Thus

Vedclass · Accepted Answer

$33$

Vedclass · Answer

(D) Let $\frac{dr}{dt} = c$ and $h = ar + b$.Given $\frac{dh}{dt} = 3 \frac{dr}{dt}$,so $a \frac{dr}{dt} = 3 \frac{dr}{dt}$,which implies $a = 3$.Thus,$h = 3r + b$.When $r = 1, h = 6$,so $6 = 3(1) + b$,which gives $b = 3$.Therefore,$h = 3r + 3 = 3(r + 1)$.The volume $V = \pi r^2 h = \pi r^2 (3r + 3) = 3\pi (r^3 + r^2)$.Differentiating with respect to $t$,$\frac{dV}{dt} = 3\pi (3r^2 + 2r) \frac{dr}{dt}$.When $r = 6$,$\frac{dV}{dt} = 1$,so $1 = 3\pi (3(36) + 2(6)) \frac{dr}{dt} = 3\pi (108 + 12) \frac{dr}{dt} = 360\pi \frac{dr}{dt}$.Thus,$\frac{dr}{dt} = \frac{1}{360\pi}$.When $r = 36$,$\frac{dV}{dt} = n = 3\pi (3(36)^2 + 2(36)) \frac{dr}{dt}$.$n = 3\pi (3888 + 72) \frac{1}{360\pi} = 3\pi (3960) \frac{1}{360\pi} = 3 	imes 11 = 33$.

Similar Questions

An aeroplane at an altitude of $1 \text{ km}$ is flying horizontally at $600 \text{ km/hr}$, passes directly over an observer. The rate at which it is approaching the observer when it is $1250 \text{ meters}$ away from him is........ (in $\text{ km/hr}$)

The radius of a circle is increasing at a rate of $0.1 \text{ cm s}^{-1}$. Then the rate of change of area,when its radius is $5 \text{ cm}$,is .........

$A$ 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 $\pi$)

$A$ man,$2 \ m$ tall,walks at the rate of $1 \frac{2}{3} \ m/s$ towards a street light which is $5 \frac{1}{3} \ m$ above the ground. At what rate is the tip of his shadow moving? At what rate is the length of the shadow changing when he is $3 \frac{1}{3} \ m$ from the base of the light?

$A$ point moves in a straight line during the time $t = 0$ to $t = 3$ according to the law $s = 15t - 2t^2$. The average velocity is

Vedclass Test Series

Exam Paper Generator

Online Exam Module