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Subject: Maths, asked on 6/8/23

36. A tank, as shown in the figure below, formed using a combination of a cylinder and a cone, offers better drainage as compared to a flat bottomed tank.

A tap is connected to such a tank whose conical part is full of water. Water is dripping out from a tap at the bottom at the uniform rate of 2 cm?/s. The semi-vertical angle of the conical tank is 45?.

On the basis of given information, answer the following questions: (i)

Find the volume of water in the tank in terms of its radius r.

Find rate of change of radius at an instant when r = 2?2 cm.

(ii)

(iii) (a) Find the rate at which the wet surface of the conical tank is decreasing at an instant when radius r = OR r = 2?2 cm.

(iii)

(b) Find the rate of change of height 'h' at an instant when slant height is 4 cm.

Subject: Maths, asked on 31/7/23

Ca foundation maths icai question

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