Home
Class 11
MATHS
If the surface area of a sphere of radiu...

If the surface area of a sphere of radius r is increasing uniformly at the rate `cm^(2)//s`, then the rate of change of its volume is :

A

costant

B

proportional to `sqrt(r )`

C

proportional to `r^(2)`

D

proportional to r

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • RATE MEASUREMENT

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE - 1) (LEVEL - 1) (STRAIGHT OBJECTIVE TYPE QUESTION)|43 Videos
  • PROPERTIES OF VECTORS

    AAKASH SERIES|Exercise PRACTICE EXERCISES|55 Videos
  • RATE OF CHANGE

    AAKASH SERIES|Exercise Advanced Subjective Type Questions|22 Videos

Similar Questions

Explore conceptually related problems

Find the volume and surface area of a sphere of radius 42 cm.

If the surface area of a sphere is 154 cm^(2), find its radius.

Find the total surface area of a hemi-sphere of radius 2.8 cm.

If the surface area of a sphere is 154 cm ^(2) , find its radius

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

If the volume of a spherical ball is increasing at the rate of 4pi cc/sec, then the rate of increases of its radius (in cm/sec), when the volume is 288pi cc.

AAKASH SERIES-RATE MEASUREMENT-PRACTICE SHEET (EXERCISE - 1) (LEVEL - 1) (STRAIGHT OBJECTIVE TYPE QUESTION)
  1. If the surface area of a sphere of radius r is increasing uniformly at...

    Text Solution

    |

  2. If a particle moves alonga straight line by S = 4t^(2) - 8t + 3 and th...

    Text Solution

    |

  3. The rate of change of sin t is n, then the rate of change of tan t is

    Text Solution

    |

  4. A particle moves along a straight line according to the equation s = 8...

    Text Solution

    |

  5. An angle theta through which a pulley turns with time 't' is completed...

    Text Solution

    |

  6. A particle moves along a line by s = (t^(3))/(3) - 3t^(2) + 8t then th...

    Text Solution

    |

  7. A particle 'p' moves along a straight line away from a point 'O' obeyi...

    Text Solution

    |

  8. If the rate of change of sine and tangent of the same angle are equal ...

    Text Solution

    |

  9. If the displacement in time t of a particle is given by s = ae^(t) + b...

    Text Solution

    |

  10. If the distance S travelled by a particle in time t is given by s = t^...

    Text Solution

    |

  11. The displacement of a particle in time 't' is given by S = t^(3) - t^(...

    Text Solution

    |

  12. A particle moves in a straight line according to the law v^(2) = 4a (x...

    Text Solution

    |

  13. The distance moved by the particle in time 't' is given by S = t^(2) -...

    Text Solution

    |

  14. A particle moves along the X-axis with velocity v = (dx)/(dt)=f(x) the...

    Text Solution

    |

  15. If the distance travelled by a particle is x = sqrt(pt^(2) + 2qt + r...

    Text Solution

    |

  16. If a particle moves along a line by S = sqrt(1 + t) then its accelerat...

    Text Solution

    |

  17. A particle moves on a line according to the law s = at^(2) + bt + c. I...

    Text Solution

    |

  18. A particle velocity v at time is given by v = 2e^(2t) cos(pi t)/(3). T...

    Text Solution

    |

  19. Each side of an equilateral triangle expands at the rate of 2 cm/sec. ...

    Text Solution

    |

  20. A variable triangle ABC is inscribed in a circle of diameter x units. ...

    Text Solution

    |

  21. An aeroplane is flying horizontally at an altitude of 3000 ft directly...

    Text Solution

    |