Any 1 here help me with calculus ?

A Conical paper cup 8 inches across the top and 6 inches deep is full of water. The cup springs a leak at the bottom and loses water at the rate of 2 cubic inches per minutes. How fast is the water level dropping at the instant when the water is exactly 3 inches deep ?

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A few days ago

qwerty u

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we have radius, r = 8/2 = 4 ; height, h = 6 ; dV/dt = 2

to find, dh/dt when h = 3

to eliminate r,

r/h =4/6 therefore, r = 2h/3

expression for v becomes,

V = 1/3 pi (2h/3)^2 h

= (4 pi h^3)/27

differentiating with respect to t,

dV/dt = 4/9 pi h^2 dh/dt

or dh/dt = 9 /(4 pi h^2) dV/dt

substituting h = 3 and dV/dt = 2,

dh/dt = 1/2 pi = 7/44 = 0.16 in/min

and there’s your answer!

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Any 1 here help me with calculus ?

Any 1 here help me with calculus ?

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