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Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
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Choose the correct answer in a cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of

\begin{array}{1 1}(A)\; 1 m^3/h & (B)\; 0.1 m^3/h \\(C)\; 1.1 m^3/h & (D)\; 0.5 m^3/h \end{array}

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1 Answer

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  • Volume=$\pi r^2 h$
Step 1:
Let $h$ be the height of the cylindrical tank at any instant .
Volume of the cylindrical tank $=\pi r^2 h$
$\qquad\qquad\qquad\qquad\quad\quad\;\;=\pi(10)^2h$
$V=100\pi h$
Rate of change of volume=$\large\frac{dV}{dt}$
$\large\frac{dV}{dt}=$$100\pi \large\frac{dh}{dt}$------(1)
The tank is filled at the rate of $314$cubic feet per minute .
(i.e)$\large\frac{dV}{dt}$$=314$
Step 2:
From (1)
$314=100\pi \large\frac{dh}{dt}$
$\large\frac{dh}{dt}=\frac{314}{100\pi}$
$\qquad=\large\frac{314}{100\times 3.14}$$=1$
Hence the depth of the tank changes at $1$ cubic ft/minute
Hence part (A) is the correct answer.
answered Aug 13, 2013 by sreemathi.v
 

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