Home
Class 12
MATHS
A cylindrical container is to be made fr...

A cylindrical container is to be made from certain solid material which the following constraints : It has a fixed inner volume of `V mm^3`, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container.
If the volume of the materia! used to make the container is minimum when the inner radius of the container is 10 mm, then the value of `V/(250pi)` is

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

A cylindrical container is to be made from certain solid material with the following constraints : It has a fixed inner volume of V "mm"^(3) , has a 2 mm thick solid wall andis open at the top. The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is 10 mm, then the value of (V)/(250pi) is-

The length of radius of base of a solid right circular cone is equal to the length of radius of a solid sphere . If the volume of the sphere is 2 times the volume of the cone , then find the ratio of the height and radius of base of the cone .

If the volume of the solid sphere be 38808 c.c, then the radius of the sphere is

If the radii and volumes of a solid right circular cone and a solid sphere be equal, then what will be the ratio of the length of diameter of the sphere and the height of the cone ?

IF the volume of a container is V, the pressure on the walls of the container by a gas is p and internal energy of the gas is U, then

The lengths of radii of a solid right crcular cone and a solid sphere are equal. If their - volumes be also equal, then find the ratio of the radius of the sphere and the height of the cone.

Show that the height of a cylinder of given total surface area and open at the top has maximum volumes is equal to the radius of its base .

A hemispherical bowl has a radius of 3.5 cm What would be the volume of water it would contains?

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The smallest positive root of the equation tanx-x=0 lies in (a)(0,pi/2...

    Text Solution

    |

  2. Let P(x)=a0+a1x^2+a2x^4+...+an x^(2n) be a polynomial in a real variab...

    Text Solution

    |

  3. A cylindrical container is to be made from certain solid material whic...

    Text Solution

    |

  4. Statement 1: If f(0)=0,f^(prime)(x)=ln(x+sqrt(1+x^2)), then f(x) is po...

    Text Solution

    |

  5. Match the items of column I with column II and select the correct opti...

    Text Solution

    |

  6. Find the points at which the function f given by f(x)=(x-5)^4 has loca...

    Text Solution

    |

  7. Find the greatest value of f(x)=1/(2a x-x^2-5a^2)in[-3,5] depending up...

    Text Solution

    |

  8. The set of all values of a for which the function f(x)=(sqrt(a+4)/(1...

    Text Solution

    |

  9. Let f(x)=(x^3-6x^2+12 x-8)e^xdot Statement 1: f(x) is neither maximum...

    Text Solution

    |

  10. Statement 1: The function f(x)=x^4-8x^3+22 x^2-24 x+21 is decreasing f...

    Text Solution

    |

  11. If f is a real function such that f(x) > 0,f^(prime)(x) is continuous ...

    Text Solution

    |

  12. Let f(x)=x^3-3x^2+6AAx in \mathbb{R} and g(x)={m a x :f(t ; x+1lt=tlt=...

    Text Solution

    |

  13. From a fixed point A on the circumference of a circle of radius r , th...

    Text Solution

    |

  14. The lower corner of a leaf in a book is folded over so as to reach the...

    Text Solution

    |

  15. h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4) where f''(x)> 0 AA x in (-3,4)...

    Text Solution

    |

  16. If 0<x1<x2<x3<pi, then prove that sin((x1+x2+x3)/3)>(sinx1+sinx2+sinx3...

    Text Solution

    |

  17. Prove: sin^2θ+cos^2θ=1

    Text Solution

    |

  18. Prove that (tan^(-1) 1/e)^2+(2e)/ sqrt(e^2+1)<(tan^(-1)e)^2+2/(sqrt(e^...

    Text Solution

    |

  19. If f(x)=x^3+bx^2+cx+d and 0ltb^2ltc then in (-oo,oo)

    Text Solution

    |

  20. The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x ...

    Text Solution

    |