The radius of a right circular cylinder increases at the rate of , and the height decreases at the rate of . The rate of change of the volume of the cylinder in , when the radius is and the height is is
The position of a moving car at time is given by , where are real numbers greater than . Then the average speed of the car over the time interval is attained at the point:
A spherical iron ball of radius is coated with a layer of ice of uniform thickness that melts at a rate of . When the thickness of ice is , then the rate (in .) at which the thickness of ice decreases, is:
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is Water is poured into it at a constant rate of Then the rate in at which the level of water is rising at the instant when the depth of water in the tank is is:
A spherical iron ball of radius is coated with a layer of ice of uniform thickness that melts at a rate of When the thickness of the ice is then the rate at which the thickness in of the ice decreases, is :
An inverted conical flask is being filled with water at the rate of . The height of the flask is and the radius of the base is . How fast is the water level rising when the level is
If the surface area of a cube is increasing at a rate of , retaining its shape; then the rate of change of its volume (in ), when the length of a side of the cube is , is:
A ladder of long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate The height of the upper end (in meters) while it is descending at the rate of is
A m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate , then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is m above the ground is:
