Home
Class 12
MATHS
An open box, with a square base, is to b...

An open box, with a square base, is to be made out of a given quantity of metal sheet of area `A^(2)` , then the maximum volume of the box is-

A

`(A^(3))/(3 sqrt(3) )`

B

`(2A^(3))/(3 sqrt(3) )`

C

`(A^(3))/(6 sqrt(3) )`

D

`(A^(3))/(2 sqrt(3) )`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 6|30 Videos
  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 7|30 Videos
  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 4|30 Videos
  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 7|80 Videos
  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 9|66 Videos

Similar Questions

Explore conceptually related problems

An open box with a square base is to be made out of a given quantity of card board of area c^(2) sq . Unit . Show that the maximum volume of the box is (c^(3))/(6sqrt(3)) cubi unit .

An open box with a square base is made out of a given iron sheet of area 27 sq.m. Then, the maximum volume of the box is-

Show that the height of a cylinder of given total surface area and open at the top has maximum volumes is equal to the radius of its base .

If the area of the base of a right circular cone be 4pi r^2 sq-cm and height be 3 cm , then the volume of the cone will be

A box with square top and bottom is to be made to contain 250 cm^(3) Material for the top and bottom costs Rs. 2 per cm^(2) and the material for the vertical sides costs Rs. 1 per cm^(2) . What is the cost of the least expensive box that can be made?

An open topped box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

The volume of an open tank with a square base of side x m is 40m^3 . Express its total surface area as a function of x.

CHHAYA PUBLICATION-MCQ ZONE 3 -Question Paper 5
  1. The normal to the curve x= a(1 + cos theta ) , y= a sin theta at the ...

    Text Solution

    |

  2. If the area bounded by the parabola y= ax^(2) and x= ay^(2) , a gt 0...

    Text Solution

    |

  3. The locus of the middle point of the intercept of the tangent drawn fr...

    Text Solution

    |

  4. Which one of the following definite integrals represents the area inc...

    Text Solution

    |

  5. A normal to the parabola y^(2)=5x makes an angle 45^(@) with the x-ax...

    Text Solution

    |

  6. If the tangents to the graph of the function y= f(x) make angle (pi)/(...

    Text Solution

    |

  7. The maximum value of xy when x+2y=8 is

    Text Solution

    |

  8. The function f(x)= tan^(-1) (sin x + cos x ), x gt 0 is always an inc...

    Text Solution

    |

  9. The points of extrema of the function f(x)= int(0)^(x)(sin t)/(t)dt i...

    Text Solution

    |

  10. The minimum value of the function f(x)= sin x + cos x is-

    Text Solution

    |

  11. The perimeter of a sector is p , then the area of the sector is maxim...

    Text Solution

    |

  12. The value of a ( a ge 3) for which the sum of the cubes of the roots ...

    Text Solution

    |

  13. If f(x)= x^(3) + (1)/(x^(3) )(x ne 0), then its greatest value is-

    Text Solution

    |

  14. The nearest point on the line 3x- 4y = 25 from the origin is

    Text Solution

    |

  15. If the slope of the tangent at (x, y) to a curve passing through the p...

    Text Solution

    |

  16. An open box, with a square base, is to be made out of a given quantity...

    Text Solution

    |

  17. If the radius of a sphere is measured as 5 m with an error of 0.02 m, ...

    Text Solution

    |

  18. If the volume of a sphere increases at a constant rate, then the rate ...

    Text Solution

    |

  19. Let A(0, 75), B(90, 0) , C(60, 40) and D(45, 25) be the corner points ...

    Text Solution

    |

  20. If f(x)= 2x^(2) + 10 x - 7 , then the approximate value of f(2.05) i...

    Text Solution

    |