Home
Class 12
MATHS
A cylindrical vessel of radius 0.5 m is ...

A cylindrical vessel of radius `0.5 m` is filled with oil at the rate of `0.25 pi  m^3`/`min`. The rate at which the surface of the oil is rising, is

A

(a) `1 m`/`min`.

B

(b) `2 m`/`min`.

C

(c) `5 m`/`min`.

D

(d) `1.25 m`/`min`.

Text Solution

Verified by Experts

The correct Answer is:
(a) `1 m`/`min`.
Given,
`r=0.5m` and `(dV)/(dt)=0.25 m^3`/`min`

We know that,
`V=pir^2h`
`(dV)/(dt)=pir^2(dh)/(dt)`
`0.25pi=pi(0.25)(dh)/(dt)`
`(dh)/(dt)=1`

Hence, correct option is a)
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|567 Videos

  • DETERMINANTS

    RD SHARMA|Exercise Solved Examples And Exercises|403 Videos

Similar Questions

Explore conceptually related problems

Base radius of a cylindrical vessel , full of oil is 30 meters. Oil is drawn from it at the rate of 27000 m^(3)//min . Rate at which level of oil in the vessel is falling is

Water is poured into an inverted conical vessel of which the radius of the base is 2m and height 4m, at the rate of 77 lit/min.The rate at which the water level is rising at the instant when the depth is 70cm is

An inverted conical vessel whose height is 10 cm and the radius of whose base is 5 cm is being filled with water at the uniform rate of 1.5cm^(3)//min . Find the rate at which the level of water in the vessel is rising when the depth is 4 cm.

A cone has a depth of 15cm and a base of 6cm radius.Water is poured into it at the rate of (16)/(5)pi cc/min. Find the rate at which the level of water in the cone is rising when the depth is 4cm.

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 (A) 1 m^3//h (B) 0.1 m^3//h (C) 1.1 m^3//h (D) 0.5 m^3//h

A cylindrical tank of radius 10m 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 (a) 1 m/hr (b) 0.1 m/hr (c) 1.1 m/h (d) 0.5 m/hr

Water is being poured on to a cylindrical vessel at the rate of 1(m^(3))/(min) .If the vessel has a circular base of radius 3m ,find the rate at which the level of water is rising in the vessel.

Oil is leaking at the rate of 16 mL/s from a vertically kept cylindrical drum containing oil. If the radius of the drum is 7 cm and its height is 60 cm, find the rate at which the level of the oil is changing when the oil level is 18 cm

The radius of a right circular cylinder increases at the rate of 0.1cm/min ,and the height decreases at the rate of 0.2cm/min . The rate of change of the volume of the cylinder,in cm^(2)/min ,when the radius is 2cm and the height is 3cm is -2p(b)-(8 pi)/(5)-(3 pi)/(5) (d) (2 pi)/(5)

RD SHARMA-DERIVATIVES AS A RATE MEASURER -Solved Examples And Exercises
  1. A particle moves in a straight line and its speed depends on time as v...

    Text Solution

    |

  2. The volume of a sphere is increasing at the rate of 3 cubic centimeter...

    Text Solution

    |

  3. The sides of an equilateral triangle are increasing at the rate of 2...

    Text Solution

    |

  4. The side of a square is increasing at the rate of 0.1cm/sec. Find th...

    Text Solution

    |

  5. The radius of a circle is increasing at the rate of 0.5cm/sec. Find ...

    Text Solution

    |

  6. The side of an equilateral triangle is increasing 10 \ cm/sec at th...

    Text Solution

    |

  7. Find the surface area of a sphere when its volume is changing at th...

    Text Solution

    |

  8. The rate of change of volume of a sphere is equal to the rate of cha...

    Text Solution

    |

  9. The amount of pollution content added in air in a city due to x-d i ...

    Text Solution

    |

  10. Side of an equilateral triangle expands at the rate of 2 cm/sec. The...

    Text Solution

    |

  11. The radius of a sphere is changing at the rate of 0.1 cm/sec. The ra...

    Text Solution

    |

  12. A cone whose height always equal to its diameter is increasing in volu...

    Text Solution

    |

  13. A cylindrical vessel of radius 0.5 m is filled with oil at the rate ...

    Text Solution

    |

  14. The radius of the base of a cone is increasing at the rate of 3 cm//mi...

    Text Solution

    |

  15. The radius of a sphere is increasing at the rate of 0.2 cm/sec. The ...

    Text Solution

    |

  16. The rate of change of volume of a sphere is equal to the rate of cha...

    Text Solution

    |

  17. If the rate of change of area of a circle is equal to the rate of ch...

    Text Solution

    |

  18. Each side of an equilateral triangle is increasing at the rate of 8c...

    Text Solution

    |

  19. The radius of a circular plate is increasing at the rate of 0.01 cm/...

    Text Solution

    |

  20. A cylindrical tank of radius 10m is being filled with wheat at the rat...

    Text Solution

    |