Water is dripping out from a conical funnel, at the uniform rate of 2 cc/sec through a tiny hole at the vertex of the funnel. When the slant height of water is 5 cm, find the rate of decrease of the slant height of the water.
Let AB = a metres be the lamp-post and PQ = b metres the boy, CP = y be his shadow at time t. Let AP = x.
Now ∆CAB and ∆CPQ are equiangular and hence similar
Let V be the volume of the water in the cone i.e. the volume of the water cone CA 'B' at any time t.
Let CO' = h, O' A' = r and CA' = I.
Let α be the semi-vertical angle of the cone. CAB where CO = 15 cm, OA = 5 cm
CO = 15 cm
OA = 5 cm
Then, 
Also, 
...(2)
From (1) and (2), we get,
...(3)
Now, 
(ii) Let A be the water surface area at any time t. Then, A = 
(iii) Let S be the wetted surface area of the vessel at any time t. Then. S = 
Now, 
A man of height 2 metres walks at a uniform speed of 5 km/h away from a lamp post which is 6 metres high. Find the rate at which the length of his shadow increases.
Let AB be the lamp-post and PQ the man, CP be his shadow at time t.
Let AP PC = y. Also AB = 6 m, PQ = 2 m. Now ∆CAB and ∆CPQ are equiangular and hence similar.
An inverted cone has a depth of 10 cm and a base of radius 5 cm. Water is poured into it at the rate of 
Find the rate at which the level of water in the cone is rising when the depth is 4 cm.
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