Home
Class 12
MATHS
A spherical iron ball 10 cm in radius is...

A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of `50 cm^(3)//`min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is :

A

`1/(18 pi) cm/min`

B

`1/(36 pi) cm/min`

C

`5/(6pi) cm/min`

D

`1/(54 pi) cm/min`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|200 Videos

Similar Questions

Explore conceptually related problems

The radius of a circular plate is increasing at the rate of 0.01cm/sec when the radius is 12 cm. Then the rate at which the area increases is

Gas is being pumped into a spherical balloon at the rate of 30 (ft)^(3)/min . Then the rate at which the radius increases when it reaches the value 15ft is

If the radius of a circle is increasing at a uniform rate of 2 cm/s, then find the rate of increase of area of circle at the instant when the radius is 20 cm.

The radius of a circle is increasing uniformly at the ratio 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

Find the time for which layer of ice 5 cm thick on the surface of a pond will increase its thickness by 0.1 cm when temperature of the surrounding air is -20^(@) C .

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when side is 10cm is

A sphere increases its volume at the rate of picc//s . The rate at which its surface area increases when the radius is 1 cm is

A spherical balloon is being inflated at the rate of 35 cc//min. The rate of increase of the surface area of the balloon when its diameter is 14 cm is...

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec.The rate at which the area is increases when the side is 10cm is

HIMALAYA PUBLICATION-APPLICATION OF DIFFERENTIATION-QUESTION BANK
  1. The normal to the curve : x=a(cos theta+theta sin theta), y = a (sin...

    Text Solution

    |

  2. Angle between the tangents to the curve y=x^(2)-5x+6 at the points (2,...

    Text Solution

    |

  3. A spherical iron ball 10 cm in radius is coated with a layer of ice of...

    Text Solution

    |

  4. A point an the parabola y^(2)=18x at which the ordinate increases at t...

    Text Solution

    |

  5. The area of the triangle formed by the co-ordinate axes and a tangent ...

    Text Solution

    |

  6. The curve y-e^(xy)+x=0 has a vertical tangent at the point :

    Text Solution

    |

  7. If the parametric equation of a curve is given by x = e^(t) cos t, y =...

    Text Solution

    |

  8. If y = 4x-5 is a tangent to the curve y^(2) = ax^(3)+b at (2,3) then

    Text Solution

    |

  9. The triangle formed by the tangent to the curve f(x)=x^(2)+bx-b at the...

    Text Solution

    |

  10. If the normal to the curve y = f(x) at the point (3, 4) makes an angle...

    Text Solution

    |

  11. If x+y=k is normal to y^(2)=12x, then k is :

    Text Solution

    |

  12. The point(s) on the curve y^(3)+3x^(2)=12y, where the tangent is verti...

    Text Solution

    |

  13. The line 2x+sqrt(6)y=2 is a tangent to the curve x^(2)-2y^(2)=4. The p...

    Text Solution

    |

  14. The angle between the curves y = sinx and y = cos x is

    Text Solution

    |

  15. If theta is the angle between the curves xy = 2 and x^(2)+4y = 0 then ...

    Text Solution

    |

  16. The angle between the curves x^(2) = 4y, y^(2) = 4x at (4,4) is

    Text Solution

    |

  17. The curves x = y^(2) and xy = a^(3) cut orthogonally at a point, then ...

    Text Solution

    |

  18. The equation of the tangent to the curve y = x^(3)-2x+1 at the point (...

    Text Solution

    |

  19. The equation of the tangent to the curve 6y=7-x^(3) at (1,1) is

    Text Solution

    |

  20. The slope of the nomal to the curve x = a(theta - sin theta), y = a(1-...

    Text Solution

    |