nice ouetion from application of derivatives

Q:- An inverted cone has a depth of 40cm and a base of radius 5cm.Water is poured into it at a rate of 1.5 cubic centimetres per minute.Find the rate at which the level of water in the cone is rising when the depth is 4cm.

3 Answers

1
Manmay kumar Mohanty ·

V=\frac{1}{3}\pi r^{2}h
\frac{dV}{dt}=\frac{d}{dt}\left(\frac{1}{3} \left(\frac{h}{8} \right)^{2}h\right)
\frac{dV}{dt}=\frac{d}{dt}\left(\frac{1}{192}\pi h^{3} \right)
\frac{dV}{dt}=\frac{1}{192}\pi 3h^{2}\frac{dh}{dt}
1.5=\frac{1}{64}\pi 16\frac{dh}{dt}
dhdt = 1.5 x 4\pi
dhdt = \frac{6}{\pi }

pehle ye kiya tha sayad usme depth 10 cm tha baki sab data same hai isliye check kar.Thik hai to yahi ans. hoga anhin to 38pihoga

1
ankit goel ·

But its answer is 1/10pie

1
Manmay kumar Mohanty ·

YAAR PLEASE CONFIRM THE DATA OF THE QUESTION ONCE AGAIN.

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