Home
Class 10
MATHS
The capacity of a cylinder vessel with ...

The capacity of a cylinder vessel with a hemisphere portion raised upward at the bottom as shown in the figure is `(pir^(2))/(3) [3h - 2r]`

Text Solution

Verified by Experts

True
We know that, capacity of cylinderical vessel `= pir^(2) h cm^(3)`
and capacity of hemisphere `= (2)/(3) pi r^(3) cm`
From the figure, capacity of the cylindrical vessel
`= pir^(2)h - (2)/(3) pir^(3) = (1)/(3) pir^(2)[3h - 2r]`
Promotional Banner

Topper's Solved these Questions

  • STATISTICS AND PROBABILITY

    NCERT EXEMPLAR|Exercise LONG ASWERS QUESTIONS|5 Videos

  • TRIANGLES

    NCERT EXEMPLAR|Exercise Triangles|57 Videos

Similar Questions

Explore conceptually related problems

The capacity of a cylindrical vessel with a hemispherical portion raised upward, at the bottom as shown in the given is (pi r ^(2))/(3) ( 3 h - 2 r).

The capacity of a cylindrical vessesl with a hemispherical portion raised upwards at the bottom as shown in the given figure is (pi r^(2))/(3) [3h - 2r] .

Consider a cuboidal vessel (2Rxx2RxxR) with as hemispherical cavity of radius R , kept at a horizontal smooth surface as shown in the figure. The vessel has very small hole of cross-sectional area "a". Now water of density rho is poured into space developed due horizontal surface adn vessel through hole very slowly. When the height of waer level is h , the vessel lifts off the surface and liquid leaks through space generated. (R=2m, rho=10^(3)kg//m^(3),m=9pi kg) . If the value of h is 5kcm , find the value of k . (Atmospheric pressure =10^(5)N//m^(2) ).

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 10 cm and its base of radius 3.5 cm. Find the total surface area of the article.

If the radius of the base and height of a cylinder and cone are each equal to r, and the radius of a hemisphere is also equal to r, then the volumes of the cone,cylinder and hemisphere are in the ratio (a) 1:2:3( b) 1:3:2( c) 2:1:3( d) 3:2:1

A water tank open at the top is hemispherical at the bottom and cylindrical above it.If radius of the hemisphere is 12m and the total capacity of the tank is 3312 pi backslash m^(3), then the ratio of the surface areas of the hemispherical and the cylindrical portions is (a) 1:1 (b) 3:5 (c) 4:5 (d) 6:5

A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is __________ m. (Assume there is no friction between the block and the hemisphere)

The height h of cylinder equals the circumference of the cylinder.In terms of h what is the volume of the cylinder? (h^(3))/(4 pi) (b) (h^(2))/(2 pi)(c)(h^(3))/(2) (d) pi h^(3)

A hemispherical cavity of radius R is created in a solid sphere of radius 2R as shown in the figure . Then y -coordinate of the centre of mass of the remaining sphere is

NCERT EXEMPLAR-SURFACE AREAS AND VOLUMES-Surface Areas And Volumes
  1. A solid ball is exactly fitted inside the cubical box of side a. T...

    Text Solution

    |

  2. The volume of the frustum of a cone is (1)/(3) pih [r(1)^(2) +r(2)^(2)...

    Text Solution

    |

  3. The capacity of a cylinder vessel with a hemisphere portion raised up...

    Text Solution

    |

  4. The curved surface area of frustum of a cone is pi//(r(1) +r(2)), wh...

    Text Solution

    |

  5. An open metallic bucket is the shape of a frustum of a cone mounted...

    Text Solution

    |

  6. Three metallic solid cubes whose edges are 3 cm ,4 cm and 5 cm melted...

    Text Solution

    |

  7. How many shots each having diameter 3 cm can be made form a cuboid...

    Text Solution

    |

  8. A bucket is in the form of a frustum of a cone and holds 28.490 lit...

    Text Solution

    |

  9. A cone of radius 8 cm and height 12 cm is divided into two parts by a ...

    Text Solution

    |

  10. 2 cubes each of volume 64"\ "c m^3 are joined end to end. Find the ...

    Text Solution

    |

  11. From a solid cube of side 7 cm, a conical cavity of height 7 cm and ...

    Text Solution

    |

  12. Two cones with same base radius 8 cm and height 15 cm are joine...

    Text Solution

    |

  13. Two solid cones A and B are placed in a cylindrical tube as shown in t...

    Text Solution

    |

  14. An ice-ceram cone full of ice-cream having radius 5 cm height 10 c...

    Text Solution

    |

  15. Mearbles of diameter 1.4 cm are dropped into a cylindrical beaker of d...

    Text Solution

    |

  16. How many spherical lead shots each 4.2 cm in diameter can be obtain...

    Text Solution

    |

  17. How many spherical bullets can be made out of a solid cube of lead ...

    Text Solution

    |

  18. A wall 24 m long, 0.4 m thick and 6 m high is constructed with the br...

    Text Solution

    |

  19. Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to b...

    Text Solution

    |

  20. A hemisphere of lead of radius 8cm is cast into a right circular co...

    Text Solution

    |