2. A container in the shape of a right circular cone of height 10cm and base radius 1cm is
catching water from a tap leaking at the rate of 0.1cm3s-1
. Find the rate at which the
surface area of water is increasing when the water is half-way up the cone
a side view show that using similar triangles, that when the depth pf the water is y, the radius of the water surface is r = 1/10 y
A = πr^2 = π/100 y^2
dA/dt = π/50 y dy/dt
V = 1/3 πr^2 y = 1/300 Ay ^3
so, when y=5,
dV/dt = 1/300 y^3 dA/dt + 1/100 Ay^2 dy/dt = 125(π/30 + 1/2) dA/dt
dA/dt = 1/((1250(π/30 + 1/2) cm^2/s
better check my mental arithmetic