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

A driver at a depth 12 m inside water (mu = 4//3) see the sky in a cone of semi-vertical angle is

If water is poured into an inverted hollow cone whose semi-vertical angel is 30^0, and 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.

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?

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.

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan^(-1 (0.5). Water is poured into it at a constant rate of 5 cubic metre per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 4 m.

The radius of a cylinder is increasing at the rate of 2 cm/sec and the height is decreasing at the rate of 3 cm/sec. The rate of change of volume when the radius is 3 cm and height is 5 cm is:

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 c m^2//m in , when the radius is 2c m and the height is 3cm is -2p (b) -(8pi)/5 -(3pi)/5 (d) (2pi)/5

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 c m^2//m in , when the radius is 2c m and the height is 3cm is -2p (b) -(8pi)/5 -(3pi)/5 (d) (2pi)/5

A water tank has the shape of an invertd circular cone with base radius 2 metres and height 4 metres. If water is being pumped into the tank at the rate of 2m^(3)//mm . Find the rate at which the water level is rising when the water is 3m deep

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