Tolong bantu Nomor 19. Aplikasi Turunan

ApLikasi TuruNan

r = 12 cm
h = 18 cm
r/h = 12/18 = 2/3
r = 2/3 h

dV/dt = 3 cm³/dtk

V = 1/3 π r² h
V = 1/3 π (2/3 h)² h
V = 1/3 π (4/9 h²) h
V = 4/27 π h³

dV/dt = 4/27 π . 3h² . dh/dt
3 = 4/9 π h² dh/dt
dh/dt = 3 × 9 . (4πh²)
dh/dt = 27/(4πh²)

Laju pertambahan tinggi air pd saat h = 5 cm :
dh/dt = 27/(4π . 5²)
dh/dt = 27/(100π) cm/dtk