Question 143

The circumference of a circle exceeds its diameter by 60 cm. The area of the circle is: Take($$\pi=\frac{22}{7}$$)

Solution

Let radius = r 

diameter = 2r 

According to question $$2\pi r = 2r +60$$

$$\Rightarrow 2\pi r - 2r = 60 $$

$$\Rightarrow 2r(\pi - 1) = 60 $$ 

$$\Rightarrow 2r (\dfrac{22}{7} -1)  = 60 $$

$$\Rightarrow 2r \times \dfrac{15}{7} = 60$$

$$\Rightarrow r = \dfrac {60\times 7} {30}$$

$$\Rightarrow r = 14 cm$$ 

Area = $$\pi r^2 $$ 

$$\Rightarrow  \dfrac {22}{7} \times 14 \times 14 $$

$$\Rightarrow 22\times 28 $$

$$\Rightarrow 616 cm^2$$ Ans 


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