Answer:
dh / dt = .13 ft / s
Explanation:
Let at height h , radius be r within the cone.
20 / 40= r / ( 40-h )
2r = 40 -h
r = (40 - h ) / 2
Volume of upper cone
V = 1/3 πr² ( 40 - h )
= 1/3 π (40 - h )² x ( 40 - h ) / 4
= 1/12 x π (40 - h )³
Differentiating on both sides
dV /dt = 1/12 x3 x π (40 - h )² dh / dt
= π (40 - h )²/ 4 dh / dt
Given
dV /dt = 80 , h = 12
80 = π / 4 x ( 40 - 12 )² dh / dt
dh / dt = .13 ft / s
