[Question] "(a) Water is being poured into a hemispherical bowl of radius 3 inch at the rate of 1 inch^3/s. How fast is the water level rising when the water is 1 inch deep ? (b) In (a), suppose that the bowl contains a lead ball 2 inch in diameter, and find how fast the water level is rising when the ball is half submerged." [Difficulty] Part (b) I can't see what to do Thanks for your help [Thoughts] solved Part (a) (a) V = (pi/3)* h^2*(3R-h) (volume of a segment of height h of a sphere) => dV/dt = pi*h*(2R-h)*dh/dt => dh/dt = 1/(pi*h*(2R-h))*dV/dt R = 3 inch ; h = 1 inch ; dV/dt = 1 inch^3/s so dh/dt = 1/(5*pi) inch/s
(b) ????
(b) ????