Home
Class 12
MATHS
The sum of the perimeters of a circle an...

The sum of the perimeters of a circle and a square is `k` , where `k` is some constant. Prove that the sum of their areas is least when the side of the square is double the radius of the circle.

Text Solution

Verified by Experts

The correct Answer is:
2r.
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    OSWAAL PUBLICATION|Exercise TOPIC - 5 MAXIMA AND MINIMA (SHORT ANSWER TYPE QUESTIONS - II)|3 Videos

  • APPLICATION OF INTEGRALS

    OSWAAL PUBLICATION|Exercise Long Answer Type Questions - II|25 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OSWAAL PUBLICATION|Exercise MVT AND ROLLE.S THEOREM ( SHORT ANSWER TYPE QUESTIONS-II)|5 Videos

Similar Questions

Explore conceptually related problems

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

Prove that sum of the squares of the side of a rhombus is equal to the to the sum of the squares of its diagonals.

Prove that the sum of the squares of the diagonals of parallelogram is equal to sum of the squares of its sides.

A is the centre of the circle and ABCD is a square. If BD = 4cm then find the radius of the circle

If the perimeter and area of a circle are numerically equal, then find the radius of the circle.

Prove that “the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides”.

If the sum of squares of two sides is equal to square of third side then DeltaABC is

Prove that "In a right triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides".

OSWAAL PUBLICATION-APPLICATIONS OF DERIVATIVES-TOPIC - 5 MAXIMA AND MINIMA (LONG ANSWER TYPE QUESTIONS - II)
  1. Prove that the height of the cylinder of maximum volume, that can be i...

    Text Solution

    |

  2. If the sum of the lengths of the hypotenues and a side of a right a...

    Text Solution

    |

  3. The sum of the perimeters of a circle and a square is k , where k is s...

    Text Solution

    |

  4. Find the area of the greatest rectangle that can be inscribed in an...

    Text Solution

    |

  5. Prove that the radius of the right circular cylinder of greatest cu...

    Text Solution

    |

  6. Show that the right-circular cone of least curved surface and given...

    Text Solution

    |

  7. Prove that the area of right-angled triangle of given hypotenuse is...

    Text Solution

    |

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

    Text Solution

    |

  9. Show that the height of a closed right circular cylinder of given s...

    Text Solution

    |

  10. Show that a cylinder of a given volume which is open at the top has...

    Text Solution

    |

  11. Find the point on the curve y^2= 2x which is at a minimum distance fro...

    Text Solution

    |

  12. Show that the semi-vertical angle of the cone of the maximum volume a...

    Text Solution

    |

  13. Show that all the rectangles with a given perimeter, the square has...

    Text Solution

    |

  14. A window has the shape of a rectangle surmounted by an equilateral ...

    Text Solution

    |

  15. Show that the volume of the greatest cylinder which can be inscribed i...

    Text Solution

    |

  16. Find the maximum area of an isosceles triangle inścribed in the ellip...

    Text Solution

    |

  17. An open tank with a square base and vertical sides is to be constru...

    Text Solution

    |

  18. A wire of length 28m is to be cut into two pieces. One of the piece...

    Text Solution

    |

  19. Two poles of height 16 m ans 22 m stand vertically on the ground 20 m ...

    Text Solution

    |

  20. The lengths of the sides of an isosceles triangle are 9+x^2,9+x^2 and ...

    Text Solution

    |