Home
Class 10
MATHS
Find the maximum volume of a cone that c...

Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.

Text Solution

Verified by Experts

Let the radius of the hemisphere = r units
Radius of the cone = radius of the hemisphere
height of the cone = radius of the hemisphere
`h = r`.....( 1 )
...
Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    RD SHARMA|Exercise All Questions|230 Videos
  • TRIANGLES

    RD SHARMA|Exercise All Questions|361 Videos

Similar Questions

Explore conceptually related problems

The volume of a solid hemisphere of radius "2cm" is

The total surface area of a solid hemisphere of radius r is

What is the volume of the largest cone that can be inscribed completely in a hollow hemisphere of radius 7 cm?

What is total surface area of a solid hemisphere whose radius is r?

What is the total surface area of a solid hemisphere whose radius is r?

Find the volume of hemisphere of radius 3.5cm.

A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is: (a) 3:2 (b) 4:1 (c) 4:3 (d) 7:4

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/(3) .

RD SHARMA-SURFACE AREAS AND VOLUMES-All Questions
  1. A solid iron rectangular block of dimensions 4.4m, 2.6m and 1m is cast...

    Text Solution

    |

  2. A led pencil consists of a cylindner of wood with a solid cylinder of ...

    Text Solution

    |

  3. Find the maximum volume of a cone that can be carved out of a solid ...

    Text Solution

    |

  4. Water is flowing at the rate of 3km/hr through a circular pipe of 20cm...

    Text Solution

    |

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

    Text Solution

    |

  6. 21 glass spheres, each of radius 2cm are packed in a cuboidal box of ...

    Text Solution

    |

  7. The slant height of a frustum of a cone is 4 cm and the perimeters ...

    Text Solution

    |

  8. Prove that the length of the tangents drawn from an external point to ...

    Text Solution

    |

  9. A well of inner diameter 14 m is dug 12 m deep. The earth taken out of...

    Text Solution

    |

  10. If the n^(t h) term of an A.P., is (2n+1), then the sum of its first...

    Text Solution

    |

  11. Tangent PQ at a point P of a circle of radius 5 cm meets a line throug...

    Text Solution

    |

  12. From a point on the ground, the angles of elevation of the bottom a...

    Text Solution

    |

  13. The roots of the quadratic equation 2x^2-x-6=0 (a)-2,3/2 (b) 2,-3...

    Text Solution

    |

  14. Find the area of the quadrilateral A B C D , in which A B=7c m ,B C=6c...

    Text Solution

    |

  15. The circumference of a circle is 22cm. The area of its quadrant (inc m...

    Text Solution

    |

  16. A hemisphereical bowl of internal diameter 36cm contains a liquid. Thi...

    Text Solution

    |

  17. How many sphereical lead shots each 4.2cm in diameter can be obtained ...

    Text Solution

    |

  18. 2 cubes each of volume 64" "c m^3 are joined end to end. Find the ...

    Text Solution

    |

  19. The diameter of a metallic sphere is 6cm. The sphere is melted and ...

    Text Solution

    |

  20. Three cubes whose edges measure 3cm, 4cm and 5cm respectively to form ...

    Text Solution

    |