Short answer questions (1/2 marks)
- Radius of a variable circle is changing at the rate of 5 cm/s. What is the radius of the circle at a time when its area is changing at the rate of 100 cm2/s2.
- Find the point on the curve y = x2 , where the rate of change of x-coordinate is equal to the rate of change of y-coordinate.
- The side of an equilateral triangle is increasing at the rate of 0.5 cm/s. Find the rate of increase of its perimeter.
- The total cost C(x), associated with the production of x units of an item is given by C(x) = 02x3 + 4x 2 +1000 . Find the marginal cost, when 5 items are produced.
- The total cost C(x) in rupees associates with the of production of x units of an item is given by.
- The total revenue received from the sale of x souvenirs in connection with ‘PEACE DAY’ is given by
R(x) = 3x 2 + 40x +10 . Find the marginal revenue when 100 souvenirs were sold.
- For the curve y = 5x -2x3 , if x increases at the rate of 2 units/s, then how fast is the slope of curve changing
when x = 3?
Long answer questions (4/6 marks)
- The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the surface area increasing when the length of an edge is 12 cm?
- The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
- An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
- A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm per second. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?
- The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
- A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.
- A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
- A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?
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