Water is dropped at the rate of 2 `m^3`/s into a cone of semi-vertical angle is `45^@` . If the rate at which periphery of water surface changes when the height of the water in the cone is 2m is d. Then the value of 5d is _____ m/sec

What is the semi-vertical angle of the cone through which a man, 12 cm under water, can see the sky?

Water is pumped out at a constant rate of 88 m^(3) /min from a conical container held with its axis vertical, if the semi-vertcal angle of the cone is 45^(@) , find the rate of deperssion of the water level when the depth of water level is 2 meters (pi = (22)/(7)) .

If water is poured into an inverted hollow cone whose semi-vertical angle is 30^0, show that its depth (measured along the axis) increases at the rate of 1 cm/s. Find the rate at which the volume of water increases when the depth is 24 cm.

A diver , at a depth of 12m in water ( mu = (4)/(3)) sees the sky in a cone of semivertical angle

Sand is pouring from a pipe at the rate of 12c m^3//sdot The falling sand forms a cone on the ground in such a way that the height of the cone is always 1/6th of the radius of the base. How fast does the height of the sand cone increase when the height in 4 cm?

Water is leaking from a conical funnel at the rate of 5 cm^3/sec. If the radius of the base of the funnel is 5 cm and the altitude is 10 cm, find the rate at which the water level is dropping when it is 2.5 cm from the top.

A man is moving away from a tower 41.6 m high at the rate of 2 m/sec. Find the rate at which the angle of elevation of the top of tower is changing, when he is at a distance of 30m from the foot of the tower. Assume that the eye level of the man is 1.6m from the ground.

Water is leaking from a conical funnel at the rate of 5cm^3//sec . If the radius of the base of funnel is 10 cm and its height is 20 cm, find the rate at which the water level is dropping when it is 5 cm from the top.

The radius of the base of a cone is increasing at the rate of 3 cm/min and the altitude is decreasing at the rate of 4 cm/min. The rate of change of lateral surface when the radius is 7 cm and altitude is 24cm is (a) 108pic m^2//min (b) 54pic m^2//min (c) 27pic m^2//min (d) none of these