Home
Class 12
MATHS
Of all the closed cylindrical cans (rig...

Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimetres, find the dimensions of the can which has the minimum surface area?

Text Solution

AI Generated Solution

To solve the problem of finding the dimensions of a closed cylindrical can with a given volume of 100 cubic centimeters that has the minimum surface area, we will follow these steps: ### Step 1: Define the Variables Let: - \( r \) = radius of the base of the cylinder (in cm) - \( h \) = height of the cylinder (in cm) ### Step 2: Write the Volume Formula ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT|Exercise EXERCISE 6.2|19 Videos
  • APPLICATION OF DERIVATIVES

    NCERT|Exercise EXERCISE 6.1|18 Videos
  • APPLICATION OF DERIVATIVES

    NCERT|Exercise EXERCISE 6.4|9 Videos
  • APPLICATION OF INTEGRALS

    NCERT|Exercise EXERCISE 8.2|7 Videos

Similar Questions

Explore conceptually related problems

Of all the closed cylindrical cans (right circular,which enclose a given volume of 100cm3, which has the minimum surface area?

Of all the closed cylinderical cans (right - circular), which enclose a given volume of : (i) 100 cubic centimeters (ii) 128pi cubic centimeters, find the dimensions of the can, which has the minimum surface area.

From all the closed right circular closed cylindrical can of volume 128 pi cm^(3), Find the dimension of can which has minimum surface area.

Amongst all open (from the top) right circular cylindrical boxes of volume 125 pi cm^3 , find the dimensions of the box which has the least surface area

A cylindrical can to be made to hold 1 litres of oil. Find the dimensions which will minimize the cost of the metal to make the can.

A closed cylindrical can has to be made with 100m^(2) of plastic. If its volume is maximum, then the ratio of its radius to the height is

The curved surface area of a hemisphere is 27.72 square cm and volume is 19.404 cubic cm, find its radius.

Show that the right circular cone of least curved surface and given volume has an altitude equal to time the radius of the base.

Find the volume of the larges right circular cone that can be cut out of a cube whose edge is 9cm.

NCERT-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Find the maximum and minimum values of x + sin2x on [0,2pi].

    Text Solution

    |

  2. It is given that at x = 1, the function x^(4) - 62x^(2) + ax + 9 attai...

    Text Solution

    |

  3. Find the maximum value of 2x^3-24 x+107 in the interval [1, 3]. Find ...

    Text Solution

    |

  4. Find the maximum and minimum values, if any, of the following functio...

    Text Solution

    |

  5. Find the maximum and minimum values, if any, of the following functio...

    Text Solution

    |

  6. Find the local maxima and local minima, if any, of the following func...

    Text Solution

    |

  7. Prove that the following functions do not have maxima or minima:(i) f...

    Text Solution

    |

  8. Find the absolute maximum value and the absolute minimum value of the...

    Text Solution

    |

  9. Find the maximum profit that a company can make, if the profit functi...

    Text Solution

    |

  10. Find both the maximum value and minimum value of 3x^4-8x^3-48 x-25 ...

    Text Solution

    |

  11. At what points in the interval [0,2pi], does the function sin 2x attai...

    Text Solution

    |

  12. What is the maximum value of the function sinx + cosx?

    Text Solution

    |

  13. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box wi...

    Text Solution

    |

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

    Text Solution

    |

  15. Prove that the volume of the largest cone that can be inscribed in a ...

    Text Solution

    |

  16. Show that the right circular cylinder of given surface and maximum vo...

    Text Solution

    |

  17. Of all the closed cylindrical cans (right circular), of a given volum...

    Text Solution

    |

  18. Show that semi-vertical angle of right circular cone of given surface...

    Text Solution

    |

  19. The point on the curve x^2=2y which is nearest to the point (0, 5) is(...

    Text Solution

    |

  20. Show that the right circular cone of least curved surface and given v...

    Text Solution

    |