Home
Class 12
MATHS
A cylindrical vessel of capacity 500 cub...

A cylindrical vessel of capacity 500 cubic metres open at the top is to be constructed. Find the dimensions of the vessel if the material used is minimum given that the thickness of the material used is 2 cm.

Text Solution

Verified by Experts

The correct Answer is:
`r = h = ((500)/(pi))^(1//3)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    ARIHANT PUBLICATION|Exercise ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 8 (E))|20 Videos
  • APPLICATION OF DERIVATIVES

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (VERY SHORT ANSWER TYPE QUESTIONS )|12 Videos
  • APPLICATION OF DERIVATIVES

    ARIHANT PUBLICATION|Exercise ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 8 (C))|14 Videos
  • AREA UNDER PLANE CURVES

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (LONG ANWER TYPE QUESTIONS)|15 Videos

Similar Questions

Explore conceptually related problems

A cylindrical open water tank with a circular base is to be made out of 30 sq metres of metal sheet. Find the dimensions so that it can hold maximum water. (Neglect thickness of sheet).

Young's modulus of the material of a wire is 9.8 x 10^10 N/m^2 and the area of cross-section of the wire is 0.012 cm^2 . Elastic limit of the material of the wire is exceeded when the strain exceeds 1/2400 . Find the maximum load that can be used to stretch the wire without causing a permanent set.

Special purpose coins each weighing 10gms are to be manufactured using two basic metals M_1 and M_2 and a mix of other metals M_3.M_1,M_2"and" M_3 cost₹500,₹800 and ₹800 and ₹50 per gram respectively. The strength of a coin demands that not more than 7 gm. of M_1 and a minimum of 3 gm of M_2 should be used. The amount of M_3 in each coin is maintained at 25% of that of M_1 .Since the demand for that coin is related to its price,formulate the LPP to find the minimum cost of a coin.

Find the quantity of electricity needed to plate a metal of 100 cm^2 area and 10^-2cm thickness using CuSO_4 solution. (density of copper = 9.94 gm//cm^3 and atomic mass = 63.5)

ARIHANT PUBLICATION-APPLICATION OF DERIVATIVES -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 8 (D))
  1. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

    Text Solution

    |

  2. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

    Text Solution

    |

  3. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

    Text Solution

    |

  4. Determine the absolute maximum and absolute minimum of the following f...

    Text Solution

    |

  5. Find extreme value of f(x).={{:((x)/(1-x^2),-1ltxlt0),(x^3-x,0lexlt2):...

    Text Solution

    |

  6. Find two numbers x and y whose sum is 15 such that xy^2 is maximum.

    Text Solution

    |

  7. If then sum of two positive numbers in constant then show that their p...

    Text Solution

    |

  8. Determine a rectangle of area 25sq. Units which has minimum perimeter.

    Text Solution

    |

  9. Find the altitude of a right circular cylinder of maximum volume inscr...

    Text Solution

    |

  10. Show that the radius of the right cicular cylinder of greatest curved ...

    Text Solution

    |

  11. Show that the semivertical angle of a cone of given slant height is ta...

    Text Solution

    |

  12. A cylindrical open water tank with a circular base is to be made out o...

    Text Solution

    |

  13. A cylindrical vessel of capacity 500 cubic metres open at the top is t...

    Text Solution

    |

  14. Find the coordinates of the point on the curve x^2y - x + y = 0 wher...

    Text Solution

    |

  15. Find the points on the curve y = x^2+1 which are nearest to the point ...

    Text Solution

    |

  16. Show that the minimum distance of a point on the curve (a^(2))/(x^(2))...

    Text Solution

    |

  17. Show that the vertical angle of a right circular cone of minimum curve...

    Text Solution

    |

  18. Show that the semi-vertical angle of a right circular cone of minimum ...

    Text Solution

    |

  19. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

    Text Solution

    |

  20. Shows that the triangle of greatest area that can be inscribed in a ci...

    Text Solution

    |