Home
Class 12
MATHS
A window is in the form of a rectangle s...

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

Text Solution

Verified by Experts

The correct Answer is:
length = `(20)/(pi+4)` m , breadth = `(10)/(pi+4)` m
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.5|48 Videos

  • APPLICATION OF INTEGRALS

    NCERT GUJARATI|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.

Find the area of four walls of a room (Assume that there are no doors or windows ) if its length 12m. Breadth 10 m. and height 7.5 m.

At a depth of 1000 m in an ocean (a) What is the absolute pressure ? (b) What is the gauge pressure ? © Find the force acting on the window of area 20cmxx20cm of a submarine at this depth the interior of which is maintained at sea level atmospheric pressure. (the density of sea water =1.03xx10^(3)xx10^(3)kgm^(-3),g=10ms^(-2))

The length, breadth and height of a hall are 16 m, 10 m and 6 m respectively. It has two doors measuring 2 m times 1.5 m each and four windows measuring 2 m times 2 m each. Find the cost of white washing all the four walls and the ceiling of the hall at the rate of Rs. 5 per m^(2) .

At a depth of 1000m in an ocean (a) What is the absolute pressure? (b) what is the gauge pressure? (c ) find the force acting on the window of area 20cm times 20 cm of a submarine at this depth, the interior of which is maintained at sea level atmospheric pressure. the density of sea water is 1.03 times 10^3 kg m^-3 . g=10 ms^-2

NCERT GUJARATI-APPLICATION OF DERIVATIVES-EXERCISE 6.6
  1. Show that the normal at any point theta to the curve x=acostheta+at...

    Text Solution

    |

  2. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

    Text Solution

    |

  3. Find the intervals in which the function f given by f(x)=\ x^3+1/(...

    Text Solution

    |

  4. Find the maximum area of an isosceles triangle inscribed in the ellip...

    Text Solution

    |

  5. A tank with rectangular base and rectangular sides, open at the top...

    Text Solution

    |

  6. The sum of the perimeter of a circle and square is k, where k is so...

    Text Solution

    |

  7. A window is in the form of a rectangle surmounted by a semicircular...

    Text Solution

    |

  8. A point on the hypotenuse of a triangle is at distance a and b from t...

    Text Solution

    |

  9. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

    Text Solution

    |

  10. Find the absolute maximum and minimum values of the function f give...

    Text Solution

    |

  11. Show that the altitude of the right circular cone of maximum volume...

    Text Solution

    |

  12. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

    Text Solution

    |

  13. Show that the height of the cylinder of maximum volume that can be ...

    Text Solution

    |

  14. Show that height of the cylinder of greatest volume which can be insc...

    Text Solution

    |

  15. A cylindrical tank of radius 10 m is being filled with wheat at the r...

    Text Solution

    |

  16. The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2) -2t -5 at...

    Text Solution

    |

  17. The line y = m x + 1is a tangent to the curve y^2=4xif the value of m...

    Text Solution

    |

  18. The normal at the point (1,1) on the curve 2y+x^2=3is(A) x + y = 0 (B)...

    Text Solution

    |

  19. The normal to the curve x^2=4ypassing (1,2) is(A) x + y = 3 (B) x y ...

    Text Solution

    |

  20. The points on the curve 9y^2=x^3, where the normal to the curve makes ...

    Text Solution

    |