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:
The volume and depth of water in a vessel are connected by the relation and the volume of water is increasing at the rate of When , the rate at which the depth of water is increasing 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 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:
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:
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:
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
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
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 :
A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of . The rate of increase of its volume when radius is is________
