Home
Class 8
MATHS
If V is the volume of a cuboid of dim...

If `V` is the volume of a cuboid of dimensions `a ,\ b ,\ c\ a n d\ S` is its surface area, then prove that `1/V=2/S(1/a+1/b+1/c)`

Text Solution

AI Generated Solution

To prove the equation \( \frac{1}{V} = \frac{2}{S} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right) \), we will start by recalling the formulas for the volume and surface area of a cuboid. ### Step-by-Step Solution: 1. **Define the dimensions of the cuboid:** Let the dimensions of the cuboid be: - Length \( a \) - Breadth \( b \) ...
Promotional Banner

Topper's Solved these Questions

  • MENSURATION-I (AREA OF A TRAPEZIUM AND A POLYGON

    RD SHARMA|Exercise All Questions|86 Videos
  • MENSURATION-III (SURFACE AREA AND VOLUME OF A RIGHT CIRCULAR CYLINDER)

    RD SHARMA|Exercise All Questions|109 Videos

Similar Questions

Explore conceptually related problems

If V is the volume of a cuboid of dimensions a,b,c and S is its surface area,then prove that (1)/(V)=(2)/(S)((1)/(a)+(1)/(b)+(1)/(c))

If V is the volume of a cuboid of dimensions a,b, candS is its surface area,then prove that (S)/(V)=2((1)/(a)+(1)/(b)+(1)/(c))

If ‘V’ is the volume of a cuboid of dimensions a xx b xx c and ‘S’ is its surface area, then prove that (1) /(V) =(2) /(5) [(1)/(a) +(1)/(b) +(1)/(c ) ] .

If V is the volume of a cuboid of dimensions x,y,z and A is its surface area,then (A)/(V)x^(2)y^(2)z^(2)( b) (1)/(2)((1)/(xy)+(1)/(yz)+(1)/(zx))(1)/(2)((1)/(x)+(1)/(y)+(1)/(z))(d)(1)/(xyz)

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14cm. If S is the sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S - 3V) equal to?

The dimension of a cuboid are 16 cm, 18 cm and 24 cm . Find : (a) volume (b) surface area (c) diagonal

RD SHARMA-MENSURATION-II (VOLUMES AND SURFACE AREAS OF A CUBOID AND A CUBE)-All Questions
  1. The outer dimensions of a closed wooden box are 10 c m\ by 8c m\ ...

    Text Solution

    |

  2. Find the length of the longest rod that can be placed in a room 12m...

    Text Solution

    |

  3. If V is the volume of a cuboid of dimensions a ,\ b ,\ c\ a n d\ S ...

    Text Solution

    |

  4. The areas of three adjacent faces of a cuboid are x, y and z. If the v...

    Text Solution

    |

  5. A rectangular water reservoir contains 105\ m^3 of water. Find the dep...

    Text Solution

    |

  6. Cubes A ,\ B ,\ C\ having edges 18cm, 24cm and 30cm respectively a...

    Text Solution

    |

  7. The breadth of a room is twice its height, one half of its length a...

    Text Solution

    |

  8. A closed iron tank 12m long, 9m wide and 4m deep is to be made. Det...

    Text Solution

    |

  9. A tank open at the top is made of iron sheet 4m wide. If the dimensi...

    Text Solution

    |

  10. Three equal cubes are placed adjacently in a row. Find the ratio of...

    Text Solution

    |

  11. The dimensions of a room are 12.5 m by 9m by 7m. There are 2 doors a...

    Text Solution

    |

  12. A field is 150m long and 100m wide. A plot (outside the field) 50m l...

    Text Solution

    |

  13. Two cubes, each of volume 512\ c m^3 are joined end to end. Find the s...

    Text Solution

    |

  14. Three metal cubes whose edges measure 3c m ,\ 4c m\ a n d\ 5c m resp...

    Text Solution

    |

  15. The cost of preparing the walls of room 12m long at the rate of Rs. ...

    Text Solution

    |

  16. The length of a hall is 18m and the width 12m. The sum of the areas ...

    Text Solution

    |

  17. A metal cube of edge 12cm is melted and formed into three smaller cu...

    Text Solution

    |

  18. The dimensions of a cinema hall are 100m, 50m and 18m. How many pers...

    Text Solution

    |

  19. The external dimensions of a closed wooden box are 48cm, 36cm, 30cm....

    Text Solution

    |

  20. The dimensions of a rectangular box are in the ratio 2:3:4 and the d...

    Text Solution

    |