A body is composed of a right cylinder and above it a semi-sphere with common base if the total surface area of the body is 2000 π 〖cm〗^2 , Find the height and the radius of the cylinder’s base, so that the volume of the body is maximum

A thin rod of length 1 m is fixed at one of its ends and was let to vibrate as a pendulum, if the resistance of the rod against breaking at any point on it is given by the relation :
R=ax(1-x)^2 where x is the distance of the point from the fixed end a<0 , Find the point at which the resistance is minimum