Home
Class 12
MATHS
Water comes out from a conical funnel at...

Water comes out from a conical funnel at the rate of `5 cm^(3)//s`. When the slant height of a water cone is 4 cm, find the rate of decrease of slant height of a water cone. The semi vertical angle of a conical funnel is `(pi)/(3)`.

Text Solution

Verified by Experts

The correct Answer is:
`(5)/(6pi)cm//s`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|83 Videos
  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK|51 Videos
  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise MISCELANEOUS EXERCISE - 6|27 Videos
  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos
  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

Water is dripping out from a conical funnel at a uniform rate of 4c m^3//s through a tiny hole at the vertex in the bottom. When the slant height of the water is 3cm, find the rate of decrease of the slant height of the water-cone. Given that the vertical angle of the funnel is 120^0dot

The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.

The volume of a right circular cone is 9856 cm^(3) . If the diameter of the base is 28 cm, find (i) height of the cone, (ii) slant height of the cone and (iii) curved surface area of the cone.

The radius and slant height of a cone are 21 cm and 35 cm respectively. Find the volume of the cone.

Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

Sand is pouring from a pipe at the rate of 12 cm^(3)//s . The falling sand forms a cone on the ground in such a way that the height of the cone is always one - sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm ?

If the volume of a right circular cone of height 9 cm is 48 pi" "cm^(3) , find the diameter of its base.

Water pours out rate of Q from a tap, into a cylindrical vessel of radius r. The rate at which the height of water level rises the height is h, is

If the slant height of a frustum of a conc is 20 cm and the radii of its circular bases are 20 cm and 8 cm respectively, find the volume of the frustum (Use pi=3.14)

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -PRACTICE WORK
  1. Water comes out from a conical funnel at the rate of 5 cm^(3)//s. When...

    Text Solution

    |

  2. A ladder 20 feet long is leaning against a wall. The bottom of the lad...

    Text Solution

    |

  3. If the height of the cone is constant then find the rate of change of ...

    Text Solution

    |

  4. A man 2m tall walks at a uniform speed of 4m/min away from a lamp pos...

    Text Solution

    |

  5. According to Boil's law PV = C, where V = 600 cm^(3), P = 150 SI/cm^(2...

    Text Solution

    |

  6. The measure of two sides of a triangle is 10 m and 15 m. The angle bet...

    Text Solution

    |

  7. A cylinder is heated in such a way that its radius always remains twic...

    Text Solution

    |

  8. A kite is flying at a height 151.5 m from horiozontal. The speed of th...

    Text Solution

    |

  9. Two trains start from the same place. A person travel in a train whose...

    Text Solution

    |

  10. The area of a triangle is increasing at the rate of 4 cm^(2)//s. Its a...

    Text Solution

    |

  11. Show that f(x)=x^(3)-6x^(2)+12x-18 is an increasing function on R.

    Text Solution

    |

  12. Find the intervals in which f(x)=(4x^(2)+1)/(x) is increasing or decre...

    Text Solution

    |

  13. Find the least value of a such that the function given by f(x)=x^(2)+a...

    Text Solution

    |

  14. Prove that f(x)=x^(2)-x sin x is increasing on (0, (pi)/(2)).

    Text Solution

    |

  15. Find the value of a for which the function f(x)=ax^(3)-3(a+2)x^(2)+9(a...

    Text Solution

    |

  16. Find the in intervals in which f(x)=sin^(4)x+cos^(4)x is increasing or...

    Text Solution

    |

  17. f : (0, pi)to R, f(x)=2x+cot x. Find the intervals in which f(x) is st...

    Text Solution

    |

  18. Show that f(x)=x^(3)-3x^(2)+4x, x in R is strictly increasing on R.

    Text Solution

    |

  19. Without using differentiation, prove that f(x)=ax+b, where a gt 0 is s...

    Text Solution

    |

  20. f : R^(+)to R^(+), f(x)=(log x)/(sqrt(x)). Find the intervals in which...

    Text Solution

    |