Home
Class 10
MATHS
A solid right circular cone of height ...

A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm.Such that it touhces the bottom .Find the volume of water of left in the cylinder, if the radius of the cylinder is equal to the radius to the cone.

Text Solution

Verified by Experts

(i) Whenever we placed a solid right circular cone in a right circular cylinder with full of water, then volume of a solid right circular cone is equal to the volume of water falled from the cylinder.
(ii) Total volume of water in a cylinder is equal to the volume of the cylinder.
(iii) Volume of water left in the cylinder = Volume of the right circular cylinder - Volume of a right circular cone.
Now, given that
Height of a right circular cone = 120 cm
Radius of a right cicrular cone = 60 cm
`therefore ` Volume of a right circular cone `= (1)/(3) pi r^(2) xxh`
`" " = (1)/(3) xx (22)/(7)xx 60 xx 60 xx 120`
`,, = (22)/(7) xx 20 xx 60 xx 120`
`= " " 144000 pi cm^(3)`
`therefore ` Volume of a right cicrular cone = Volume of water falled from the cylinder
`,, =144000 pi cm^(3)" "["from point(i)"]`
Given that, height of a right circular cylinder = 180 cm
and radius of a right circular cylinder = Radius of a right circular cone = 60 cm
`therefore` Volume of a right cirular cylinder `= pir^(2) xx h`
`" " = pi xx 60xx60xx180`
`" "= 648000 pi cm^(3)`
So, volume of a right cylinder = Total volume of water of water in a cylinder
`" "= 648000 pi cm^(3) " "["form point(ii)"]`
Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    NCERT EXEMPLAR ENGLISH|Exercise SHORT ANSWER TYOE QUESTIONS|14 Videos
  • STATISTICS AND PROBABILITY

    NCERT EXEMPLAR ENGLISH|Exercise LONG ASWERS QUESTIONS|14 Videos
  • TRIANGLES

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|18 Videos

Similar Questions

Explore conceptually related problems

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

A solid consisting of a right standing on a hemisphere is placed upright in a right circular cylinder full of water and touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm, the radius of the hemisphere is 60 cm and height of the cone is 120 cm, assuming that the hemisphere and the cone have common base.

A solid consisting of a right circular cone, standing on a hemisphere, is placed upright, in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm, the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer correct to the nearest centimetre ( Take pi = 3 (1)/(7))

From a right circular cylinder with height 10cm and radius of base 6cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid.

From a right circular cylinder with height 10cm and radius of base 6cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid.

From a right circular cylinder with height 10cm and radius of base 6cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid.

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49cm. Find the radius of the base.

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49cm. Find the radius of the base.

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49cm. Find the radius of the base.

NCERT EXEMPLAR ENGLISH-SURFACE AREAS AND VOLUMES-LONG ANSWER TYPE QUESTIONS
  1. A hemisphere of lead of radius 8cm is cast into a right circular co...

    Text Solution

    |

  2. A rectangular water tank of base 11 m xx 6m contains water upto a...

    Text Solution

    |

  3. How many cubic cm of iron is required to construct open box whose ext...

    Text Solution

    |

  4. The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5...

    Text Solution

    |

  5. Water flows at the rate of 10 meter per minute through a cylindrical p...

    Text Solution

    |

  6. A heap of wheat is in the form of a cone of diameter 9 m and height ...

    Text Solution

    |

  7. A factory manufacture 120000 pencils daily. The pencils are cylindri...

    Text Solution

    |

  8. Water is flowing at the rate of 15 km/hour through a pipe of diameter ...

    Text Solution

    |

  9. A solid iron rectangular block of dimensions 4.4 m , 2.6 m and 1 m is ...

    Text Solution

    |

  10. 500 persons have to dip in a rectangular tank which is 80 m long an...

    Text Solution

    |

  11. Metal sphere, each of radius 2 cm, are packed into a rectangular ...

    Text Solution

    |

  12. A milk container of height 16 cm is made of metal sheet in the form...

    Text Solution

    |

  13. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is ...

    Text Solution

    |

  14. A rocket is in the form of a right circular cylinder closed at the ...

    Text Solution

    |

  15. A bulinding is in the form of a cylinder surmounted by a hemispheri...

    Text Solution

    |

  16. A hemispherical bowl of internal radius 9 cm is full of liquid . The ...

    Text Solution

    |

  17. A solid right circular cone of height 120 cm and radius 60 cm is pl...

    Text Solution

    |

  18. A water flows through a cylindrical pipe, whose inner radius is 1 cm...

    Text Solution

    |

  19. The rain water from a roof af dimensions 22 m xx 20 m drains into ...

    Text Solution

    |

  20. A pen stand made of wood is in the shape of a cuboid with four ...

    Text Solution

    |