Home
Class 10
MATHS
An open box is to be made from a square ...

An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown in figure. Express volume V of the box as a function of x.

Text Solution

Verified by Experts

The correct Answer is:
`4x^(3)-96x^(2)+576x`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    SURA PUBLICATION|Exercise EXECRISE 1.4|29 Videos
  • RELATIONS AND FUNCTIONS

    SURA PUBLICATION|Exercise EXECRISE 1.5|19 Videos
  • RELATIONS AND FUNCTIONS

    SURA PUBLICATION|Exercise EXECRISE 1.2|9 Videos
  • ONE MARK QUESTIONS SET

    SURA PUBLICATION|Exercise Multiple Choice Question|250 Videos
  • STATISTICS AND PROBABILITY

    SURA PUBLICATION|Exercise Unit Test (Section -C)|1 Videos

Similar Questions

Explore conceptually related problems

We have a 12 square unit piece of thin material and want to make an open box by cutting small squares from the corners of our material and folding the sides up. The question is, which cut produces the box of maximum volume ?

A box, constructed from a rectangular metal sheet, is 21 cm by 16cm by cutting equal squares of sides x from the corners of the sheet and then turning up the projected portions. The value of x os that volume of the box is maximum is (a) 1 (b) 2 (c) 3 (d) 4

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.

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 ?

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 closed box (cuboid) with a square base is to have a volume 2000c.c, The material for the top and bottom of the box is to cost Rs 3 per square cm and the material for the sides is to cost Rs 1.50 per square cm. If the cost of the material is to be least find the dimension of the box.

A piece of paper is in the shape of a square of side 1m long. It is cut at the four corners to make a regular polygon of eight sides (octagon). The area of the polygon is

A metal box with a square base and vertical sides is to contain 1024 cm3 of water, the material for the top and bottom costs Rs 5 per cm2 and the material for the sides costs Rs 2.50 per cm2. Find the least cost of the box.

SURA PUBLICATION-RELATIONS AND FUNCTIONS-EXECRISE 1.3
  1. Given the function f:x to x^(2)-5x+6, evaluate f(-1)

    Text Solution

    |

  2. Given the function f:x to x^(2)-5x+6, evaluate f(2a)

    Text Solution

    |

  3. Given the function f:x to x^(2)-5x+6, evaluate f(2)

    Text Solution

    |

  4. Given the function f:x to x^(2)-5x+6, evaluate f(x-1)

    Text Solution

    |

  5. A graph representing the function f(x) is given in figure it is clear ...

    Text Solution

    |

  6. A graph representing the function f(x) is given in figure it is clear ...

    Text Solution

    |

  7. A graph representing the function f(x) is given in figure it is clear ...

    Text Solution

    |

  8. A graph representing the function f(x) is given in figure it is clear ...

    Text Solution

    |

  9. Let f(x)=2x+5. If xne0 then find (f(x+2)-f(2))/(x)

    Text Solution

    |

  10. A function is defined by f(x)=2x-3 Find (f(0)+f(1))/(2).

    Text Solution

    |

  11. A function is defined by f(x)=2x-3 Find x such that f(x)=0.

    Text Solution

    |

  12. A function is defined by f(x)=2x-3 Find x such that f(x)=x.

    Text Solution

    |

  13. A function is defined by f(x)=2x-3 Find x such that f(x)=f(1-x).

    Text Solution

    |

  14. An open box is to be made from a square piece of material, 24 cm on a ...

    Text Solution

    |

  15. A function f is defined by f(x)=3-2x. Find x such that f(x^(2))=(f(x))...

    Text Solution

    |

  16. a plane is flying at a speed of 500 km per hour. Express the distance ...

    Text Solution

    |

  17. The data in the adjcent table depicts the length of a woman's forehead...

    Text Solution

    |

  18. The data in the adjcent table depicts the length of a woman's forehead...

    Text Solution

    |

  19. The data in the adjcent table depicts the length of a woman's forehead...

    Text Solution

    |

  20. The data in the adjcent table depicts the length of a woman's forehead...

    Text Solution

    |