1) The total surface area of a hemisphere is decreasing at a rate of 2cm^2/s. Find the rate of change of the volume of the hemisphere when its radius is 1/2cm.
2) Sand is poured into a right circular cone at the rate of 18cm^3/s, of which the height is three-quarters its radius. Calculate the instant when the radius is 6cm, the rate of change of
i) its radius
ii) the area of the area.
Sorry, I wanted to ask why for the first question I have to express volume in terms of surface area and then use the chain rule, dV/dt = dV/dA * dA/dt. How come I cannot find the dr/dt first by using dA/dt = dA/dr * dr/dt. After i got the dr/dt, I use dV/dt = dV/dr * dr/dt. But the answer is different.
However for the second question part ii, i do not need to express volume in terms of area. I just have to use dA/dr * the part (i) answer dr/dt. I am a bit confused when i should express something in terms of something. Thanks.