Asked by Sally
Mulch is dumped into a pile with height always 1/3 the diameter at a rate of 30 ft^3/hr. How fast is the height increasing when it is 6 ft tall?
Answers
Answered by
Steve
h = d/3, so d = 3h
v = π/3 r^2 h = π/3 (3h/2)^2 h = 3π/4 h^3
dv/dt = 9π/4 h^2 dh/dt
so,
9π/4 * 6^2 dh/dt = 30
v = π/3 r^2 h = π/3 (3h/2)^2 h = 3π/4 h^3
dv/dt = 9π/4 h^2 dh/dt
so,
9π/4 * 6^2 dh/dt = 30
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