EASY
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If the edge of a variable cube is increasing at the rate of  3 cm/sec, the rate of increase of the volume of the cube when the edge is 10 cm long is :

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Important Questions on Application of Derivatives

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Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder in cm3/min, when the radius is 2 cm and the height is 3 cm is
EASY
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
The sides of an equilateral triangle are increasing at the rate of 4 cm/sec. The rate at which its area is increasing, when the side is 14 cm
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
The position of a moving car at time t is given by f(t)=at2+bt+c, t>0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval t1,t2 is attained at the point:
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
Let f( x+y )=f( x )f( y ) for all x and y. Then what is f ′ ( 5 ) equal to [ where f ′ ( x ) is the derivative of fx]?
HARD
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is tan-112. Water is poured into it at a constant rate of 5 cubic m/min. Then the rate (in m/min), at which the level of water is rising at the instant when the depth of water in the tank is 10 m; is:
EASY
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
If the side of a cube is increased by 5%, then the surface area of a cube is increased by
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
If the surface area of a cube is increasing at a rate of 3.6cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec), when the length of a side of the cube is 10cm, is:
HARD
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3/min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :
EASY
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
A 2m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25cm/sec , 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 1 m above the ground is:
EASY
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
The radius of a circle is increasing at the rate 2 cm/sec. The rate at which its area is increasing, when the radius of the circle is 5 decimeters, is
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
If the volume of spherical ball is increasing at the rate of 4π cm3/sec then the rate of change of its surface area when the volume is 288π cm3 is
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Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
The displacement of a particle at the time t is given by s=1+t, then its acceleration a is proportional to
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Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
An inverted conical flask is being filled with water at the rate of 3 cm3 sec-1. The height of the flask is 10 cm and the radius of the base is 5 cm. How fast is the water level rising when the level is 4 cm?
HARD
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
A ladder of 5 m 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 3 m/sec. The height of the upper end (in meters) while it is descending at the rate of 4 m/sec, is
EASY
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
A ladder 20ft long leans against a vertical wall. The top end slides downwards at the rate of 2ft per second. The rate at which the lower end moves on a horizontal floor when it is 12ft from the wall is
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
A point is in motion along a hyperbola y=10x so that its abscissa x increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate when the point passes through (5, 2)
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Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
A spherical iron ball of 10cm radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm3/min . When the thickness of ice is 5cm , then the rate (in cm/min .) at which the thickness of ice decreases, is:
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
If the volume of a spherical ball is increasing at the rate of 4π cc/sec then the rate of increase of its radius in cm/sec, when the volume is 288π cc is 
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Derivative as Rate of Change
A man 6 ′ tall moves away from a source of light 20 ′ above the ground level, his rate of walking being 4m/h. At what rate is the tip of his shadow moving?