Question

A conical cup is 4 cm across and 6 cm deep water leaks out of the bottom at the rate of 2 cm cubed / s. How fast is the water level dropping when the height of the water is 3 cm

Answer 1

Answer: When the height of the water is 3cm, the water level would drop at the rate of 7/11 cm per sec .

Step-by-step explanation:

Given that,

D= 4 cm

R= 2 cm

H= 6 cm

Rate of decrease in volume of a conical cup= 2 cm^3

We know,

r/h=R/H=2/6=1/3

r=1/3*h    equation 1

Volume of conical cup= 1/3*pi*r^2*h

We have

dV/dt= -2

d(1/3*pi*r^2*h)/dt= -2

Putting the value of r from equation 1 in the above differential equation. We get:

d(1/3*pi*(1/3*h)^2*h)/dt= -2

d(1/27*pi*h^3)/dt= -2

Differentiating the above equation with respect to t. We get:

1/27*pi*3h^2dh/dt= -2

1/9*pi*h^2dh/dt= -2

dh/dt= -18/(pi*h^2)

Putting h=3 cm in the above equation, we get:

dh/dt = -18/(pi*3^2)

dh/dt = -7/11