Home
Class 12
MATHS
The volume of the cylindrical trunk of a...

The volume of the cylindrical trunk of a tree is proportional to the cube of its diameter and the diameter increases uniformly from year to year,prove that the rate of increase in the volume when the diameter is equal to `90 cm` is 25 times the ratewhen it is `18 cm.`

Promotional Banner

Topper's Solved these Questions

  • Application of dy/dx

    A DAS GUPTA|Exercise Exercise|45 Videos
  • Application of Vectors

    A DAS GUPTA|Exercise Exercise|13 Videos
  • Binomial Theorem for Positive Integrel Index

    A DAS GUPTA|Exercise Exercise|113 Videos

Similar Questions

Explore conceptually related problems

The volume of the cylindrical trunk of a tree is proportional to the cube of its diameter and the diameter increases uniformly from year to year,prove that the rate of increase in the volume when the diameter is equal to 90cm is 25 xx the ratewhen it is 18cm.

If the side of a cube is increasing at the rate of 2 cm/sec.Then,what is the rate of increase in the volume when the side is 3 cm

The volume of a cylindrical vessel with diameter 8 cm and height 4 cm is

If the edge of a cube increases at the rate of 60cm per second, at what rate the volume in increasing when the edge is 90cm

If the edge of a cube increases at the rate of 60 cm per second, at what rate the volume is increasing when the edge is 90 cm

If the surface area of a sphere of radius ris increasing uniformly at the rate 8((cm)^(2))/(s), then the rate of change of its volume is:

The radius of a soap - bubble is increasing at the rate of 0.7cm//s . Find the rate of increase of : its volume when the radius is 5 cm.

Diameter and altitude of a right circular cylinder are 20 cm and 30 cm respectively .If the diameter is increasing at the rate of 4 cm//sec ., then the rate of change in its altitude when the volume is constant is

The diameter of a circle is increasing at the rate of 1 cm/sec. When its radius is pi , the rate of increase of its area, is

A DAS GUPTA-Application of dy/dx-Exercise
  1. Show that for any point of the curve x^2 - y^2 = a^2 the segment of th...

    Text Solution

    |

  2. Use calculus to find the conditiion that the line xcos theta + ysin th...

    Text Solution

    |

  3. The volume of the cylindrical trunk of a tree is proportional to the c...

    Text Solution

    |

  4. A stick of length 100 cm rests against a vertical walland the horizont...

    Text Solution

    |

  5. A man running along a circular track has the speedof 10 km per hour. A...

    Text Solution

    |

  6. A point is moving along the curve y^(3)=27x. The interval in which the...

    Text Solution

    |

  7. A particle is moving along the parabola y^2 = 12x at the uniform rate ...

    Text Solution

    |

  8. A spherical balloon is being inflated so that itsvolume increases unif...

    Text Solution

    |

  9. The time t of a complete oscillation of a simple pendulum of length l ...

    Text Solution

    |

  10. The time t of a complete oscillation of a simple pendulum of length l ...

    Text Solution

    |

  11. A spherical iceball is melting, such that the radius is decreasing at ...

    Text Solution

    |

  12. Use differentials to obtain a resonable approximation to (8. 01)^(4/3)...

    Text Solution

    |

  13. Let C be the curve y^(3) - 3xy + 2 =0. If H is the set of points on th...

    Text Solution

    |

  14. A spherical rain drop evaporates at a rate proportional to its surf...

    Text Solution

    |

  15. The law of rectilinear motion of a body of mass 10kg is given by s = ...

    Text Solution

    |

  16. The slope of the tangent to the curve r^2 = a^2 cos 2theta, where x = ...

    Text Solution

    |

  17. A balloon is pumped at the rate of 10 cu cm/min. The rate of increase ...

    Text Solution

    |

  18. If the line a x+b y+c=0 is a normal to the curve x y=1, then a >0,b >...

    Text Solution

    |

  19. The angle between the curves y = sinx and y = cosx is

    Text Solution

    |

  20. The point on the ellips 9x^(2) +16y^(2)=400 at which the abscissa and ...

    Text Solution

    |