Home
Class 12
MATHS
Sand is pouring from a pipe at the rate ...

Sand is pouring from a pipe at the rate of 12 cubic cm./sec. 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. At which rate is the height of the sand-cone increasing when the height is 4 cm. ?

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(48pi)` cm /s
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT TELUGU|Exercise EXERCISE 6.2|22 Videos

  • APPLICATION OF DERIVATIVES

    NCERT TELUGU|Exercise EXERCISE 6.3|31 Videos

  • APPLICATION OF DERIVATIVES

    NCERT TELUGU|Exercise EXERCISE 6.6|22 Videos

  • APPLICATION OF INTEGRALS

    NCERT TELUGU|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

The slant height of a cone is fixed as 7 cm. If the rate of increase in tis height os 0.3 cm/sec, then the rate of increase of volume when height 4 cm is

The radius of the base and height of a cone are 5 cm and 12 cm then its slant height

Sand is being poured on the ground from the orifice of an elevated pipe and from a pile which has always the shape of a right circular cone whose height is equal to the radius of the base. If the sand if falling at the rate of 1000 cubic cm per, sec, the rate at which the height of the pile is rising when the height is 40 cm is

Sand is being poured on the ground from the orifice of an elevated pipe and forms a pile which has always the shape of a right circular cone whose height is equal to the radius of the base. If the sand is falling at the rate of 6 cubic ft per sec, the rate at which the height of the pile is rising when the height is 5 ft is

The radius of the base of a cone is 14 cm and its height is 24 cm. Find the volume

The radius of the circular disc increases at a uniform rate of 0.025 cm per sec. The rate at which the area of the disc increases, when the radius is 15 cm is

The radius and slant height of a cone are 8 cm and 17 cm respectively. Then its height is

A ballon is in the shape of a cone surmounted by a semi sphere. The radius of a sphere is equal to the height of the cone. If the height of the ballon is 2 then the rate of change in its volume is ……..times the rate of change in its height.

The slant height of a cone is fixed at 7cm. The rate of increase in the volume of the cone corresponding to the rate of increases of 0.3 cm/s in the hieght when h = 4cm is

NCERT TELUGU-APPLICATION OF DERIVATIVES-EXERCISE 6.1
  1. Find the rate of change of the area of a circle with respect to its ra...

    Text Solution

    |

  2. The volume of a cube is increasing at a rate of 8 cubie centimeters pe...

    Text Solution

    |

  3. The radius of a circle is increasing uniformly at the rate of 3 cm/s. ...

    Text Solution

    |

  4. An edge of a variable cube is increasing at the rate of 3 cm/s. How fa...

    Text Solution

    |

  5. A stone is dropped into a quiet lake and ripples move in circles at th...

    Text Solution

    |

  6. The radius of a circle is increasing at the rate of 0.7 cm/s. What is ...

    Text Solution

    |

  7. The length x of a rectangle is decreasing at the rate of 5 cm/minute a...

    Text Solution

    |

  8. A balloon which always remains spherical on inflation is being inflate...

    Text Solution

    |

  9. A balloon, which always remains spherical has a variable radius. Find ...

    Text Solution

    |

  10. A ladder 5 m long is leaning against a wall. The bottom of the ladder ...

    Text Solution

    |

  11. A particle moves along the curve 6y = x^(3) +2. Find the points on the...

    Text Solution

    |

  12. The radius of an air bubble is increasing at the rate of 1/2 cm/sec. A...

    Text Solution

    |

  13. A balloon, which always remains spherical, has a variable diameter (3)...

    Text Solution

    |

  14. Sand is pouring from a pipe at the rate of 12 cubic cm./sec. The falli...

    Text Solution

    |

  15. The total cost C(x) in Rupees associated with the production of x unit...

    Text Solution

    |

  16. The total revenue in Rupees received from the sale of x units of a pro...

    Text Solution

    |

  17. The rate of change of the area of a circle with respect to its radius ...

    Text Solution

    |

  18. The total revenue in Rupees received from the sale of x units of a pro...

    Text Solution

    |