# RATE OF CHANGE ( CALCULUS) FOR 12th GRADE / A & AS LEVEL Online Test

The sides of an equilateral triangle are increasing at the rate of 2 cm / sec . At what rate will its area be increasing when its side is 10 cm ?

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 m^3 per hour . At what rate will the depth of the wheat be increasing ?

A ladder 5 m long is leaning against a wall.

The bottom of the ladder is pulled along the ground , away from the walll, at the rate of 2 m / sec .

How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

Two parallel sides of a rectangle are being legthened at the rate of 2 cm / sec while the other two sides are shortened in such a way that the figure remains a rectangle with constant area 50 cm^2 .

What is the rate of change of its perimeter when the legth of the increasing side is 10 cm ?

A stone is dropped into a quiet lake and the waves move in a circle at a speed of 4 cm/sec.

At the instant when the radius of the circular wave is 10 cm , the enclosed area increases at the rate of ...........

A spherical balloon is being inflated so that its volume increases uniformly at the rate of 40 cm^3 / minute

When the radius is 8m , its surface area is increasing at the rate of .......................

A man 2 m high walks at a uniform speed of 5 m / min away from a lamp-post 6 m high.

The rate at which the length of his shadow increases is .......................

Volume of a sphere is increasing at a constant rate with respect to time.

Then the rate at which its radius is increasing is ....................

A water tank has a rectangular base 1.5 m by 1.2 m.

The sides are vertical and water is being added to the tank at a constant rate of 0.45 m^3 per minute

At what rate is the depth of the water in the tank increasing ?

The rate of change of the circumference of a circle is 0.3 cm / sec

How fast is its area increasing when its radius is 5 cm ?

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This serves as a practice test for students who are doing Differentiation at their Senior secondary School level.

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