Home
Class 12
MATHS
A stone is dropped into a quiet lake and...

A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing ?

Text Solution

Verified by Experts

The correct Answer is:
`80 pi cm^(2)//cm`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)|24 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (LONG ANSWER TYPE QUESTIONS)|10 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|83 Videos

  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos

  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

A stone is dropped into a quiet lake and waves move in circles spreading out radially at the speed of 0.5m//s . At the instant when the radius of the circular wave is (4)/(pi) m, how fast is the enclosed area (in m^(2//s) ) increasing ?

The surface area of a spherical bubble is increasing at the rate of 2 c m^2//s . When the radius of the bubble is 6cm, at what rate is the volume of the bubble increasing?

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

The radius of a circular plate increase at the rate of 0.1 cm per second. At what rate does the area increase when the radius of plate is 5/pi cm ?

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increases when the edge is 10 cm long ?

The diagonal of a suare is increasing at the rate of 0.5 cm/sec. when the area of a square is 400 cm^(2) , the area is increasing at the rate of ………….

An edge of a variable cube is increasing at the rate of 3 cm//s . How fast is the volume of the cube increasing when the edge is 10 cm long?

A car moves with constant speed of 10 m/s in a circular path of radius 10m. The mass of the car is 1000 kg. How much is the required centripetal force for the car?

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK
  1. Find the rate of change of the area of a circle per second with respec...

    Text Solution

    |

  2. The volume of a cube is increasing at a rate of 9 cubic centimetres pe...

    Text Solution

    |

  3. A stone is dropped into a quiet lake and waves move in circles at the ...

    Text Solution

    |

  4. The length x of a rectangle is decreasing at the rate of 5 cm/minute a...

    Text Solution

    |

  5. The total cost C(x) in Rupees associated with the production of x unit...

    Text Solution

    |

  6. The total revenue in Rupees received from the sale of x units of a pro...

    Text Solution

    |

  7. Show that the function given by f(x)=7x-3 s increasing on R.

    Text Solution

    |

  8. Show that the function f given by f(x)=x^(3)-3x^(2)+4x, x in R is incr...

    Text Solution

    |

  9. Prove that the function given by f (x)=cos x (a) Decreasing in (0, ...

    Text Solution

    |

  10. Find the intervals in which the function f given by f(x)=x^(2)-4x+6 is...

    Text Solution

    |

  11. Find the intervals in which the function f given by f(x)=4x^(3)-6x^(2)...

    Text Solution

    |

  12. Find intervals in which the function given by f(x)=sin 3x, x in [0, (p...

    Text Solution

    |

  13. Find the intervals in which the function f given by f(x)=sin x + cos x...

    Text Solution

    |

  14. Find the slope of the tangent to the curve y=x^(3)-x at x = 2.

    Text Solution

    |

  15. Find the point at which the tangent to the curve y=sqrt(4x-3)-1 has it...

    Text Solution

    |

  16. Find the equation of all lines having slope 2 and being tangent to the...

    Text Solution

    |

  17. Find points on the curve (x^(2))/(4)+(y^(2))/(25)=1 at which the tange...

    Text Solution

    |

  18. Find the equation of the tangent to the curve y=(x-7)/((x-2)(x-3)) at ...

    Text Solution

    |

  19. Find the equations of the tangent and normal to the curve x^((2)/(3))+...

    Text Solution

    |

  20. Find the equation of tangent to the curve given by x=a sin^(3)t, y=b c...

    Text Solution

    |