Home
Class 12
MATHS
A spherical balloon is filled with 4500p...

A spherical balloon is filled with 4500pi cubic metres of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72pi cubic metres per minute, then the rate (in metres per minute) at which the radius of the balloon decreases 49 minutes after the leakage begins is :

A

`9/7`

B

`7/9`

C

`2/9`

D

`9/2`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE|433 Videos
  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise EXERCISE|211 Videos

Similar Questions

Explore conceptually related problems

The bottom of a rectangular swimming tank is 25 m by 40m. Water is pumped into the tank at the rate of 500 cubic metres per minute. Find the rate at which the level of water in the tank is rising.

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cm^3 0f gas per sec. Find the rate at which the radius of the balloon increases when the radius is 15 cm.

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of:

In a competition, a brave child tries to inflate a huge spherical balloon bearing slogans against child labour at the rate of 900 cubic centimeter of gas per second. Find the rate at which the radius of the balloon is increasing when its radius is 15 cm. Also write any three value/life skill reflected in this question.

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank. The water is collected in a cylindrical vessel, radius of whose base is 60 cm. find the rise in the level of water in 30 minutes?

Water flows a the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the surface is 40 cm and depth 24cm^2 .

MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Let f: R rarr R be a positive increasing function with underset(xrar...

    Text Solution

    |

  2. Let F: R rarr R be defined by: f(x) = {:{(k-2x,ifxle-1),(2x+3,ifx> -1)...

    Text Solution

    |

  3. A spherical balloon is filled with 4500pi cubic metres of helium gas. ...

    Text Solution

    |

  4. The real number k for which the equations 2x^3 +3x+k=0 has two distinc...

    Text Solution

    |

  5. The number of points in (-oo,oo) for which x^(2)-xsinx-cosx=0, is

    Text Solution

    |

  6. The normal to the curve x^(2)+2xy-3y^(2)=0 at (1, 1)

    Text Solution

    |

  7. Let f(x) be a polynomial of degree four having extreme values at x =1 ...

    Text Solution

    |

  8. Consider f(x) = tan^-1(sqrt((1+sinx)/((1-sinx)))), x in (0,pi/2) A nor...

    Text Solution

    |

  9. A wire of the length 2 units is cut into two parts which are bent resp...

    Text Solution

    |

  10. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

    Text Solution

    |

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

    Text Solution

    |

  12. Show that the function f given by, f(x) = x^3 - 3x^2 + 4x, x in R is i...

    Text Solution

    |

  13. Find the slope of the tangent to the curve y = x^3-3x+2 at the point w...

    Text Solution

    |

  14. A man of height 2m walks at a uniform speed of 5km/h away from a lamp...

    Text Solution

    |

  15. Find the intervals in which the function given by : f (x) = sin x + co...

    Text Solution

    |

  16. Prove that the curves x = y^2 and xy = k cut at right angles if 8k^2 =...

    Text Solution

    |

  17. Evaluate sqrt(401), using differentials.

    Text Solution

    |

  18. It is given that at x = 1, the function x^4 - 62x^2 + ax + 9 attains i...

    Text Solution

    |

  19. Find the equations of the tangents to the curve 3x^2 - y^2 = 8, which ...

    Text Solution

    |

  20. Show that the height of the cylinder of maximum volume that can be ins...

    Text Solution

    |