JEE Main 2022 · 27 Jul · Shift 2 · Mathematics Q25

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MathematicsInteger+4 / -1Question 25 of 90

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is $\tan^{-1}\dfrac34$ . Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is ______.

Your answer

Answer and worked solution

Official answer: 5

Cone. $r=\frac34h$ , so $V=\frac{3\pi h^3}{16}$ and the curved area is $S=\pi r\cdot\frac54h=\frac{15\pi h^2}{16}$ .

Rates at h = 4. $9\pi\frac{dh}{dt}=6$ , and $\frac{dS}{dt}=\frac{15\pi}2\cdot\frac2{3\pi}=5$ .

Answer: 5

Topics:Rate of change

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JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 25