Question

Suppose the radius of the cylinder is decreasing at a rate of 2 cm/sec, but the volume is constant. How fast is the height changing when the radius is 10 cm and the height is 35 cm? Include units with your answer. Hint: If the volume is constant, what do you know about the rate of change of the volume?

Answer 1

Answer:

Height is increasing at the rate of 14cm/s.

Step-by-step explanation:

Volume of cylinder = π$R^2*H$

dR/dT = -2cms (-ve sign indicated decreasing rate)

we need to find

dH/dT = ?

as the volume remain constant,  that means the cylinder is decreasing in area but its increasing in height.

dV/dT=0 (volume remain constant)

dV/dT= 2πR*dR/dT *H + π$R^2$*dH/dT = 0

2π*10*(-2)*35 + π*10*10 * dH/dT = 0

-1400π + 100πdH/dT = 0

dH/dT= 1400π/100π

dH/dT = 14 Cm/s

This means the height is increasing at the rate of 14cm/s.