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The area of a circle is increased by 22 sq. cm if its radius is increased by 1 cm. The original radius of the circle is :
Answer & Solution
Correct Answer:
Option
A
Let the original radius of the circle be R cm
Then,
$$\eqalign{ & \pi \left[ {{{\left( {R + 1} \right)}^2} - {R^2}} \right] = 22 \cr & \Rightarrow \left( {2R + 1} \right) = \frac{{22 \times 7}}{{22}} \cr & \Rightarrow 2R + 1 = 7 \cr & \Rightarrow 2R = 6 \cr & \Rightarrow R = 3\,cm \cr} $$
Then,
$$\eqalign{ & \pi \left[ {{{\left( {R + 1} \right)}^2} - {R^2}} \right] = 22 \cr & \Rightarrow \left( {2R + 1} \right) = \frac{{22 \times 7}}{{22}} \cr & \Rightarrow 2R + 1 = 7 \cr & \Rightarrow 2R = 6 \cr & \Rightarrow R = 3\,cm \cr} $$
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