Answer:
13π/2 m²/h
Step-by-step explanation:
Volume of a cylinder is:
V = πr²h
If h is a constant, then taking derivative of V with respect to time:
dV/dt = 2πrh dr/dt
Surface area of a cylinder is:
A = 2πr² + 2πrh
Taking derivative with respect to time:
dA/dt = (4πr + 2πh) dr/dt
Given that dV/dt = 10π, V = 80π, and h = 5, we need to find dA/dt. But first, we need to find r and dr/dt.
V = πr²h
80π = πr² (5)
r = 4
dV/dt = 2πrh dr/dt
10π = 2π (4) (5) dr/dt
dr/dt = 1/4
dA/dt = (4πr + 2πh) dr/dt
dA/dt = (4π (4) + 2π (5)) (1/4)
dA/dt = 13π/2
The surface area of the cylinder is increasing at 13π/2 m²/h.
