Try this:
- assuming that h is a constant (is it?)
, so
mm/min = 0.01 cm/min.
.
Engine cylinder 15 cm deep, being bored out
radius increases by .10 mm/min
How fast does volume change when dia is 9.5 cm?
pi(r^2)h = V
pi(4.25)^2(15) = 851.12 cm^3
dr/dt = .01 cm
dv/dt = ?
f'gh + fg'h + fgh'
f' = pi
g' = 2r(dr/dt)
h' = dh/dt
pi(4.25^2)(15) + (pi)((4.25)(0.01) + (pi)(r^2)(1) = 911.91 cm^3
which is very wrong. Where did I go wrong? thanks.
Well, you could use the chain rule, but it's a bit of overkill to apply to constants:
Since and h are constants their derivatives are both zero, giving you: