Home
Class 12
MATHS
A balloon, which always remains spherica...

A balloon, which always remains spherical, has a variable diameter `3/2(2x+1)`.Find the rate of change of its volume with respect to x.

Text Solution

Verified by Experts

The correct Answer is:
`(27)/(8) pi (2x+1)^(2)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.2|23 Videos
  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.3|31 Videos
  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.6|24 Videos
  • APPLICATION OF INTEGRALS

    NCERT GUJARATI|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

A balloon, which always remains spherical, has a variable diameter (3)/(2)(2x+1) . Find he rate of change of its volume with respect to x.

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

Find the derivative of the following functions with respect to x tan (2x+3)

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.

Given that y=sin3x+(4)/(3)cos3x . What is the maximum rate of change in y with respect to x ?

Assertion :- A particle has positive acceleration it means that its speed always increases. Reason :- Acceleration is the rate of change of speed with respect to time.

Radius of a spherical balloon is increasing with respect to time at the rate of 2//pi" "m//s . Find the rate of change in volume (in m^(3)//s ) of the balloon when radius is 0.5 m?

A cylinder is heated in such a way that its radius always remains twice of its height when the radius is 3 cm, find the rate of increase of its volume. The radius is increased at the rate of 2 cm/s. Also find the rate of increase of its total surface area.

x and y are the sides of two squares such that y=x-x^(2) . Find the rate of change of the area of second square with respect to the area of first square.

NCERT GUJARATI-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 the rate of 8 c m^3//s. How fast...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. A stone is dropped into a quiet lake and waves move in circles at the ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. The radius of an air bubble is increasing at the rate of 1/2c m//s. 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 of12\ c m^3//s . The falling s...

    Text Solution

    |

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

    Text Solution

    |

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

    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 pr...

    Text Solution

    |