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

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 minimizes the 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 Equation ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|24 Videos
  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6.4|9 Videos
  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

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

Amongst all open (from the top) right circular cylindrical boxes of volume 125pi cm^3 , find the dimensions of the box which has the least 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 closed right circular cylinder has volume 539/2 cubic units. Find the radius and the height of the cylinder so that the total surface area is minimum.

A right circular cone has a volume of 24pi cubic inches. If the height of the cone is 2 inches, what is the radius, in inches, of the base of the cone?

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

Show that the semi vertical angle of a right circular cone of given total surface area and max volume is sin^-1 (1/3)

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

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

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

NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Exercise 6.5
  1. Find the maximum value of 2x^3-24 x+107in the interval [1, 3]. Find t...

    Text Solution

    |

  2. It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...

    Text Solution

    |

  3. Find the maximum and minimum values of f(x)=x+sin2x in the interval...

    Text Solution

    |

  4. Find two numbers whose sum is 24 and whose product is as large as p...

    Text Solution

    |

  5. Find two positive numbers x and y such that x+y=60 and x y^3 is max...

    Text Solution

    |

  6. Find two positive numbers x and y such that their sum is 35 and ...

    Text Solution

    |

  7. Find two positive numbers whose sum is 16 and the sum of whose cube...

    Text Solution

    |

  8. A square piece of tin of side 18 cm is to be made into a box w...

    Text Solution

    |

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

    Text Solution

    |

  10. Show that of all the rectangles inscribed in a given circle, the sq...

    Text Solution

    |

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

    Text Solution

    |

  12. Of all the closed cylindrical cans (right circular), of a given volume...

    Text Solution

    |

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

    Text Solution

    |

  14. Prove that the volume of the largest cone, that can be inscribed in...

    Text Solution

    |

  15. Show that right circular cone of least curved surface and given volume...

    Text Solution

    |

  16. Show that semi-vertical angle of a cone of maximum volume and given sl...

    Text Solution

    |

  17. Show that the semi vertical angle of a right circular cone of given ...

    Text Solution

    |

  18. The point on the curve x^2=2ywhich is nearest to the point (0, 5) is(A...

    Text Solution

    |

  19. For all real values of x, the minimum value of (1-x+x^2)/(1+x+x^2)is(...

    Text Solution

    |

  20. The maximum value of [x(x-1)+1]^(1/3), 0 le x le 1 is:

    Text Solution

    |