Home
Class 12
MATHS
A water tank has the shape of an inve...

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is `tan^(-1)(0. 5)` . Water is poured into it at a constant rate of 5 cubic metre per hour. Find the rate at which

Text Solution

Verified by Experts

The correct Answer is:
`(35)/(88)` m/h
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CBSE COMPLEMENTARY MATERIAL|Exercise 6 MARK QUESTIONS|13 Videos

  • APPLICATION OF DERIVATIVES

    CBSE COMPLEMENTARY MATERIAL|Exercise 2 MARK QUESTIONS|20 Videos

  • APPLICATIONS OF INTEGRALS

    CBSE COMPLEMENTARY MATERIAL|Exercise FOUR/SIX MARK QUESTIONS|26 Videos

Similar Questions

Explore conceptually related problems

A water tank has the shape of an inverted righ circular cone with its axis vertical and vertex lowermost . Its semi-vertical angle is tan^(-1)(0.5) . Water is poured into it at a constant rate of 4 cubic meter per hour . Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 2 m.

A water tank has the shape of an inverted right - circular cone with its axis vertical and vertex lower most. Its semi - vertical angle is tan^(-1)((1)/(2)) . Water is poured into it at a constant rate of 5 cubic meter per minute. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 10 m.

A water tank has a shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan^(-1)((3)/(4)) . Water is poured into it at a constant rate of 3 cubic meter per hour .The rate at which the level of the water is rising at an instant when the depth of water in the tank is 4m is

A water tank has a shape of an inverted right circular cone with its axis vertical and vertex lower-most. Its semi-vertical angle is tan^(-1)((3)/(4)) . Water is poured into it at a constant rate of 3 cubic meter per hour. The rate at which the level of the water is rising at an instant when the depth of water in the tank is 4m is

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is tan ^(-1)((1)/(2)) . Water is poured into it at a constant rate of 5 cu m/min. Then, the rate (in m/min) at which the level of water is rising at the instant when the depth of water in the tank is 10 m is

A water tank has the shape of a right circular cone with its vertex down. Its altitude is 10 cm and theradius of the base is 15 cm. Water leaks out of the bottom at a constant rate of lcu.cm/sec. Water ispoured into the tank at a constant rate of C cu. cm/sec. Compute C so that the water level will berising at the rate of 4 cm/sec at the instant when the water is 2 cm deep.

A water tank has the shape of a cube with each side of length 3 metre. Water is poured into it at a constant rate of 27 cubic metre per hour. Then,the rate at which the level of the water is rising at the instant, when the depth of water in the tank is x, (0 < x < 2), is (in metre per hour) (i)x (ii) 3x (iii) 9x (iv) 3

If the lateral surface of right circular cone is 2 times its base , then the semi-vertical angle of the cone must be :

CBSE COMPLEMENTARY MATERIAL-APPLICATION OF DERIVATIVES-4 MARK QUESTIONS
  1. A swimming pool is to be drained by cleaning. If L represents the n...

    Text Solution

    |

  2. A man of 2 metres height walks at a uniform speed of 6 km/hr away from...

    Text Solution

    |

  3. A water tank has the shape of an inverted right circular cone with ...

    Text Solution

    |

  4. A spherical ball of salt is dissolving in water in such a manner that ...

    Text Solution

    |

  5. A conical vessel whose height is 10 meters and the radius of whose bas...

    Text Solution

    |

  6. xa n dy are the sides of two squares such that y=x-x^2 . Find the rate...

    Text Solution

    |

  7. The length of a rectangle is increasing at the rate 3.5 cm/sec. and it...

    Text Solution

    |

  8. If the area of circle increases at a uniform rate, then prove that the...

    Text Solution

    |

  9. Show that f(x)=x^(3)-6x^(2)+18x+5 is an increasing function for all x ...

    Text Solution

    |

  10. Determine whether the following function is increasing or decreasing i...

    Text Solution

    |

  11. Determine for which values of x, the function y=x^(4)-(4x^(3))/(3) is ...

    Text Solution

    |

  12. Find the interval of increasing and decreasing of the function f(x) =(...

    Text Solution

    |

  13. Find the intervals in which function f(x) = sin x-cos x, 0 lt x lt 2pi...

    Text Solution

    |

  14. Show that f(x)=x^(2)e^(-x), 0 le x le 2 is increasing in the indicated...

    Text Solution

    |

  15. Prove that y=(4sintheta)/((2+costheta)-theta is an increasing function...

    Text Solution

    |

  16. Find the intevals in which the following functionis decreasing. f(x) =...

    Text Solution

    |

  17. Find the interval in which the function f(x)=5x^((3)/(2))-3x^((5)/(2))...

    Text Solution

    |

  18. Show that f(x)=tan^(-1)(sinx+cosx) is an increasing function on the ...

    Text Solution

    |

  19. Find the interval in which the function f(x) =cos^(-1) ((1-x^(2))/(1+x...

    Text Solution

    |

  20. Find intervals in which the function given by f(x)=3/(10)x^4-4/5x^3-3x...

    Text Solution

    |