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Application Of Derivatives

Question
CBSEENMA12035054
Wired Faculty App

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 

  • 1 m3/h

  • 0 · 1 m3/h
  • 1 · 1 m3/h
  • 0·5 m3/ h

Solution

A.

1 m3/h

Let h be the height of the cylindrical tank at any time t.
Volume space of space the space cylindrical space tank space space equals space πr squared straight h therefore space space space space space space space straight V space equals space straight pi left parenthesis 10 right parenthesis squared straight h space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space space straight r space equals space 10 space metres close square brackets therefore space space space space space space space straight V space equals space 100 space straight pi space straight h therefore space space space space space space dV over dt space equals space 100 straight pi space dh over dt because space space space space tank space is space being space filled space with space wheat space at space the space rate space of space 314 space cubic space metre space per space hour therefore space space space space space space space space space space space 314 space equals space 100 space straight pi space dh over dt therefore space space space space space space space space space space dh over dt space equals space fraction numerator 314 over denominator 100 space straight pi end fraction space equals space fraction numerator 314 over denominator 100 space cross times space space 3.14 end fraction space equals space 314 over 314 space equals space 1 therefore space space space space space depth space of space the space wheat space increasing space at space the space rate space of space 1 space straight m cubed divided by straight h therefore space space space space space space space left parenthesis straight A right parenthesis space is space correct space answer.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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