Home
Class 12
MATHS
Find the rate of change of the total sur...

Find the rate of change of the total surface area of a cylinder of radius `r` and `h ,` when the radius varies.

Text Solution

Verified by Experts

`s=2 pi r^{2}+2 pi rh`

`frac{ds}{dr}=4 pi r+2 pi h`

rate of change `=2 pi(2 r+h)`

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|567 Videos
  • DETERMINANTS

    RD SHARMA|Exercise Solved Examples And Exercises|403 Videos

Similar Questions

Explore conceptually related problems

Find the rate of change of the total surface area of a cylinder of radius and height , when the radius varies.

The total surface area of a solid hemisphere of radius r is

The total surface area of a cylinder of base radius r and height h is______.

Write the ratio of total surface area to the surface area of a cylinder of radius r and height h

Find the surface area and total surface area of a hemisphere of radius 21cm.

Total surface area of a cylinder of radius h and height r is _________

Find the total surface area of a cylinder with radius 21 cm and height 5 cm.

Find the rate of change of the area of a circle with respect to its radius r when r=5cm.

Curved surface area of a cylinder of radius h and height r is _______.

RD SHARMA-DERIVATIVES AS A RATE MEASURER -Solved Examples And Exercises
  1. Find the rate of change of the volume of a sphere with respect to its ...

    Text Solution

    |

  2. Find the rate of change of the volume of a sphere with respect to its ...

    Text Solution

    |

  3. Find the rate of change of the total surface area of a cylinder of ...

    Text Solution

    |

  4. The money to be spend for the welfare of the employees of a firm is...

    Text Solution

    |

  5. A balloon in the form of a right circular cone surmounted by a hemi...

    Text Solution

    |

  6. Water is running into an inverted cone at the rate of pi cubic metr...

    Text Solution

    |

  7. If y=7x-x^3 and x increases at the rate of 4 units per second, how fas...

    Text Solution

    |

  8. Find an angle theta (i) Which increases twice as fast as its cosin...

    Text Solution

    |

  9. The top of a ladder 6 metres long is resting against a vertical wal...

    Text Solution

    |

  10. A ladder 13m long leans against a wall. The foot of the ladder is p...

    Text Solution

    |

  11. A particle moves along the curve y=x^2+2xdot At what point(s) on the c...

    Text Solution

    |

  12. The length x of a rectangle is decreasing at the rate of 5 cm/minut...

    Text Solution

    |

  13. A man 2 metres high walks at a uniform speed of 5 km/hr away from a la...

    Text Solution

    |

  14. The radius of a spherical soap bubble is increasing at the rate of 0.2...

    Text Solution

    |

  15. The side of a square in increasing at the rate of 0.2 cm/sec. Find the...

    Text Solution

    |

  16. An edge of a variable cube is increasing at the rate of 3cm per second...

    Text Solution

    |

  17. The side of a square sheet is increasing at the rate of 4cm per minute...

    Text Solution

    |

  18. A kit is 120m high and 130 m of string is out. If the kite is movin...

    Text Solution

    |

  19. Find the point on the curve y^2dot 8xdot for which the abscissa and or...

    Text Solution

    |

  20. A particle moves along the curve y=(2/3)x^3+1. Find the points on ...

    Text Solution

    |