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

A water tank has the shape of an invertd circular cone with base radius 2 metres and height 4 metres. If water is being pumped into the tank at the rate of `2m^(3)//mm`. Find the rate at which the water level is rising when the water is 3m deep

Text Solution

Verified by Experts

The correct Answer is:
`2=(8)/(9pi) m//min`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DIFFERENTIAL CALCULUS

    FULL MARKS|Exercise EXERCISE - 7.10|20 Videos
  • APPLICATIONS OF INTEGRATION

    FULL MARKS|Exercise ADDITIONAL PROBLEMS|35 Videos

Similar Questions

Explore conceptually related problems

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 the level of the water is rising at the instant when the depth of water in the tank is 4 m.

A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm.

A conical water tank with vertex down of 12 meters height has a radius of 5 meters at the top. If water flows into the tank at a rate 10 cubic m/min, how fast is the depth of the water increases when the water is 8 metres deep?

If water is poured into an inverted hollow cone whose semi-vertical angel is 30^0, and its depth (measured along the axis) increases at the rate of 1 cm/s. Find the rate at which the volume of water increases when the depth is 24 cm.

An overhead water tanker is in the shape of a cylinder has capacity of 61.6 cu.mts. The diameter of the tank is 5.6 m. Find the height of the tank.

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of

The refractive index of water is (4)/(3) and speed of light in air is 3xx10^(8)m//s . Find the speed of light in the water.

FULL MARKS-APPLICATIONS OF DIFFERENTIAL CALCULUS -ADDITIONAL QUESTIONS SOLVED
  1. A water tank has the shape of an invertd circular cone with base radiu...

    Text Solution

    |

  2. A car A is travelling from west at 50 km/hr and car B is travelling to...

    Text Solution

    |

  3. The distance x metres travelled by a vehicle in time t seconds after t...

    Text Solution

    |

  4. At a particular instant ship A is 100 km west of ship B, ship A is sai...

    Text Solution

    |

  5. Gravel is being duped from a conveyor belt at a rate of 30 ft^(3)//min...

    Text Solution

    |

  6. Prove that the sum of the intercepts on the co-ordinate axes of any ta...

    Text Solution

    |

  7. Find the equation of normal to y = x^(3) -3x that is parallel to 2x + ...

    Text Solution

    |

  8. Prove that the curves 2x^(2)+4y^(2)=1 and 6x^(2)-12y^(2)=1 cut each ot...

    Text Solution

    |

  9. Show that the equation of the normal to the curve x=a cos ^(3) theta, ...

    Text Solution

    |

  10. If the curve y^(2) = x and xy = k are orthogonal then prove that 8k^(2...

    Text Solution

    |

  11. Verify Rolle's theorem for the following f(x) = x^(3) -3x + 3 " in "...

    Text Solution

    |

  12. Suppose that f(0) = -3, and f' (x) le 5 for all values of x how large ...

    Text Solution

    |

  13. Using Rolle's theorem find the point on the curve y=x^(2)+1,-2lexle2 w...

    Text Solution

    |

  14. Find 'C' of Lagrange's mean value theorem for the function f(x)=2x^(3)...

    Text Solution

    |

  15. Find 'C' of Lagrange's mean value theorem for the function f(x) =x^(3)...

    Text Solution

    |

  16. The Taylor's series expension of f(x)=sin x "about" x=(pi)/(2) is obta...

    Text Solution

    |

  17. Obatin the Maclaurin's series expansion for the following function . ...

    Text Solution

    |

  18. Evaluate underset(x rarr (pi)/(2))(lim) (log sin x)/((pi - 2x)^(2))

    Text Solution

    |

  19. Evaluate: underset (xrarr0) lim (cot x) ^(sin x)

    Text Solution

    |

  20. underset (x rarr infty) lim(log x^(x))/(x)

    Text Solution

    |