Coffee is draining from a conical filter,with | vedclass

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

Question

(D) The volume of coffee in the cylindrical pot is given by $V = \pi r^2 h$,where $r$ is the radius and $h$ is the height of the coffee level.Given th

Vedclass · Accepted Answer

$\frac{16}{9\pi}$

Vedclass · Answer

(D) The volume of coffee in the cylindrical pot is given by $V = \pi r^2 h$,where $r$ is the radius and $h$ is the height of the coffee level.Given the diameter of the pot is $15 \, cm$,the radius $r = \frac{15}{2} \, cm$.Since the pot is cylindrical,the radius $r$ remains constant as the level rises,so $\frac{dr}{dt} = 0$.Differentiating the volume with respect to time $t$,we get:$\frac{dV}{dt} = \pi r^2 \frac{dh}{dt}$.We are given $\frac{dV}{dt} = 100 \, cm^3/min$.Substituting the values:$100 = \pi \left( \frac{15}{2} ight)^2 \frac{dh}{dt}$$100 = \pi \left( \frac{225}{4} ight) \frac{dh}{dt}$$\frac{dh}{dt} = \frac{100 	imes 4}{225 \pi} = \frac{400}{225 \pi} = \frac{16}{9 \pi} \, cm/min$.Thus,the rate at which the level in the pot is rising is $\frac{16}{9 \pi} \, cm/min$.

Similar Questions

$A$ closed conical vessel is filled with water fully and is placed with its vertex down. The water is let out at a constant speed. After $21 \, min$,it was found that the height of the water column is half of the original height. How much more time in minutes does it require to empty the vessel?

The rate of change of volume of a sphere with respect to its surface area when the radius is $4 \text{ cm}$ is

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

The side of an equilateral triangle expands at the rate of $2 \, cm/s$. The rate of increase of its area when each side is $10 \, cm$ is:

Two men $A$ and $B$ start with velocities $v$ at the same time from the junction of two roads inclined at $45^{\circ}$ to each other. If they travel by different roads,find the rate at which they are being separated.

Vedclass Test Series

Exam Paper Generator

Online Exam Module