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(i) The radius of a circle is increasing...

(i) The radius of a circle is increasing at the rate of 5 cm/sec. Find the rate of increasing of its perimeter.
(ii) If the area of a circle increases at a constant rate, then show that the rate of increase of its circumference is inversely proportional to its circumference is iversely proportional to its radius.

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The correct Answer is:
`10 pi cm//sec`
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NAGEEN PRAKASHAN-APPLICATIONS OF DERIVATIVES-Exercise 6a
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  2. (i) The radius of a circle is increasing at the rate of 5 cm/sec. Fin...

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  3. The side of a square is increasing at a rate of 3 cm/sec. Find the rat...

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  4. The side of a square is increasing at a rate of 4cm/sec. Find the rate...

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  5. The rate of increase of the radius of an air bubble is 0.5 cm/sec. Fin...

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  6. A balloon which always remains spherical, is being inflated by pump...

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  7. The volume of cube is increasing at a rate of 9 cm^(3)//sec. Find the ...

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  8. The volume of a spherical balloon is increasing at a rate of 25 cm^(3...

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  9. The surface of a spharical balloon is increase of its volume when its ...

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  10. The length of a rectangle is decreasing at a rate of 3 cm/sec and brea...

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  11. Find the point on the curve y^2dot 8xdot for which the abscissa and or...

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  13. The base of a cubical tank is 25 m xx 40 m. The volume of water in the...

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  14. The oil is leaking from a drum at a rate of 16 cm^(3)//sec. If the rad...

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  15. The water is leaking from a conical funnel at a rate of 5cm^(3)//min. ...

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  16. A man of height 160 cm walks at a rate of 1.1 m/sec from a lamp post w...

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  17. The total cost C(x) in Rupees, associated with the production of x ...

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  18. The total revenue of selling of x units of a product is represented by...

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  19. A ladder is inclined to a wall making an angle of 30° with it. A man i...

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  20. The one end of a 20 m long ladder is on the floor and the other end i...

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