Home
Class 12
MATHS
A sphere of radius 100mm shrinks to radi...

A sphere of radius `100mm` shrinks to radius 98mm, then the approximate decrease in its volume is (a)`12000pim m^3` (b) `80000 pim m^3` (C) `8000pim m^3` (d) `120pim m^3`

Text Solution

AI Generated Solution

To find the approximate decrease in the volume of a sphere when its radius changes, we can use the formula for the volume of a sphere and apply the concept of differentials. ### Step-by-Step Solution: 1. **Identify the volume formula**: The volume \( V \) of a sphere with radius \( r \) is given by: \[ V = \frac{4}{3} \pi r^3 ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    RD SHARMA ENGLISH|Exercise All Questions|646 Videos
  • DIFFERENTIATION

    RD SHARMA ENGLISH|Exercise All Questions|806 Videos

Similar Questions

Explore conceptually related problems

A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is 12000\ pi\ m m^3 (b) 800\ pi\ m m^3 (c) 80000\ pi\ m m^3 (d) 120\ pi\ m m^3

The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.

The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball is 50pi\ c m^2 (b) 60pi\ c m^2 (c) 75pi\ c m^2 (d) 100pi\ c m^2

The area of the floor of a room is 15\ m^2dot If its height is 4 m, then the volume of the air contained in the room is (a) 60\ d m^3 (b) 600\ d m^3 6000\ d m^3 (d) 60000\ d m^3

The ratio of the base radius and height of a cone is 5 : 12. Find its slant height and radius if its volume is 800 pi m^(3) .

If the radius of a sphere is measured as 7 m with an error or 0.02 m, find the approximate error in calculating its volume.

If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

The largest sphere is cut off from a cube of side 6cm. The volume of the sphere will be 27 pi\ c m^3 (b) 36pi\ c m^3 (c) 108pi\ c m^3 (d) 12pi\ c m^3

A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity is (a) 176\ m^3 (b) 196\ m^3 (c) 200\ m^3 (d) 110\ m^3

RD SHARMA ENGLISH-DIFFERENTIALS, ERRORS AND APPROXIMATIONS-All Questions
  1. While measuring the side of an equilateral triangle an error of k% i...

    Text Solution

    |

  2. The height of a cylinder is equal to the radius. If an error of alpha%...

    Text Solution

    |

  3. A sphere of radius 100mm shrinks to radius 98mm, then the approximate ...

    Text Solution

    |

  4. If (log)e4-1. 3868 ,t h e n(log)e 4.01= 1.3968 (b) 1.3898 (c) 1.38...

    Text Solution

    |

  5. Find the percentage error in calculating the volume of a cubical box i...

    Text Solution

    |

  6. The approximate value of (33)^(1/5) is

    Text Solution

    |

  7. Use differentials to approximate sqrt(25. 2)

    Text Solution

    |

  8. The circumference of a circle is measured as 28cm with an error of ...

    Text Solution

    |

  9. If y=x^4-10 and if x changes from 2 to 1.99, what is the approximat...

    Text Solution

    |

  10. A circular metal plate expands under heating so that its radius inc...

    Text Solution

    |

  11. Find the percentage error in calculating the volume of a cubical bo...

    Text Solution

    |

  12. The time t of a complete oscillation of a simple pendulum of length l ...

    Text Solution

    |

  13. Find the approximate change in the volume V of a cube of side x met...

    Text Solution

    |

  14. If the radius of a sphere is measured as 9 cm with an error of 0.03...

    Text Solution

    |

  15. Find the approximate value of f(3. 02) , where f(x)=3x^2+5x+3 .

    Text Solution

    |

  16. Find the approximate volume of metal in a hollow spherical shell wh...

    Text Solution

    |

  17. Use differentials to approximate sqrt(25. 2) .

    Text Solution

    |

  18. Use differentials to approximate the cube root of 127.

    Text Solution

    |

  19. Use differentials to find the approximate value of sqrt(0. 037) .

    Text Solution

    |

  20. Use differentials to find the approximate value of (log)e(4. 01), havi...

    Text Solution

    |