(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

Monjur Alahi

(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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Correct Answer - `10 pi cm//sec`

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How fast the area of a circle increases when its radius is 5cm. (i) respect to radius (ii) with respect to diameter.

(i)`A =pir^(2) ," "(dA)/(dr) =2pir` `:. (dA)/(dr)]_(r=5) " " =10 pi cm^(2)//cm.` `(ii) A =(pi)/(4) D^(2) , (dA)/(dD) =(pi)/(2)D` `:. (dA)/(dD)]_(D=10)=(pi)/(2). 10=5pi cm^(2)//cm.`

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`y=sqrt((1-sin 2x)/(1+ sin 2x))=(cos x - sin x)/(cos x + sin x)=(1-tan x)/(1+ tan x)=tan ((pi)/(4)-x)` `therefore (dy)/(dx)=-sec^(2)((pi)/(4)-x)`

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Area of circle = πr2  But area is given to be 25π sq.cm.  ∴ 25π = πr2  ∴ r2 = 25  ∴ r = 5 cm Perimeter of sector = 2r + S  But perimeter is...

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Area of circle = πr2  But area is given to be 25π sq.cm. ∴ 64π = πr2  ∴ r2 = 64  ∴ r = 8 cm Perimeter of sector = 2r + S  But perimeter is given...

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