Q.10 The area of a circle is increasing at the uniform rate of 5cm² per minute. Calculate the rate, in centimeter per minute, at which the radius is increasing when the circumference of the circle is 40cm.
Q.11 A kite is 112 meters above the ground and has 130 meters string out. If the kite is travelling horizontally at 8m/s directly away from the boy who is flying it, at what rate is the string out?
Q.12 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 2cm/sec. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?
Q.13 Water is dripping out from a conical funnel, at the uniform rate of 2 cm³/s through a tiny hole at the vertex of the bottom. When the slant height of the water is 4 cm find the rate of decrease of the slant height of the water given that the vertical angle of the funnel is 60 degree.
Q.14 The side of an equilateral triangle is a cm long and is increasing at the rate k cm/hr. how fast is the area increasing?
Q.15 The diameter and altitude of a right circular cylinder are found at a certain instant to be 10 cm and 20 cm respectively. If the diameter is increasing at the rate of 2cm. per sec, what change in the altitude will keep the volume constant?
Q.16 The radius of the base of a certain cone is increasing at the rate of 3cm per minute and the altitude is decreasing at the rate of 4 cm per minute. Find the rate of change of total surface of the cone when the radius is 7 cm and the altitude is 24 cm.