Aconical paper cup is 10 cm tall with a radius of 10 cm. the bottom of the cup ispunctured so that the water leaks out at a rate of 16p3 cm³/sec. at what rate is the waterlevel changing when the water level is 3 cm?

0.59 cm

Explanation:

height of cup (h) = 10 cm

radius of cup (r) = 10 cm

rate of change of water level (V') = 16π/3

rate of change of height (h) = 3 cm

the ratio of the height to radius (h:r) = 10:10

h/r = 10/10

h/r = 1

r=h

formula for volume of a volume (v) = .πh

substituting r=h into the formula above we have

v = .π. h = .π

differentiating the above we have

v' = 3(π)h' = π.h'

rearranging the above we have

h' = v' / (π)

where

h' = ((16 x π) / 3) ÷ ( π x )

h' = ((16 x 3.142) / 3) ÷ ( 3.142 x )

h' = 16.76 / 28.28

h' = 0.59 cm