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Sum of the diamters of two circles is 35 cm and difference of their circumferences is 22 cm. Then area of the smaller circle will be

A) 121 sq. cm
B) 144 sq. m
C) 154 sq. cm
D) 308 sq. m

Correct Answer:



C) 154 sq. cm

Description for Correct answer:
Let \( \Large r_{1} \), \( \Large r_{2} \) be the radii of two circles, then hypothesis

\( \Large 2r_{1}+2r_{2}=35 \)

=> \( \Large r_{2}+r_{1}=\frac{35}{2}=17.5 \) ...(i)

and \( \Large 2 \pi \left(r_{2}-r_{1}\right)=22 \)

=> \( \Large r_{2} - r_{1} = \frac{22}{2 \pi }=\frac{22 \times 7}{2 \times 22}=3.5 \) ...(ii)

Subtracting equation (ii) from (i), we get

\( \Large 2r_{1}=14 \)

=> \( \Large r_{1}= 7 cm\ and\ r_{2}=10.5 cm \)

Area of smaller circle = \( \Large \pi r_{1}^{2} \)

= \( \Large \frac{22}{7} \times \left(7\right)^{2} = 154\ sq.cm. \)

Part of solved Loci and concurrency questions and answers : >> Elementary Mathematics >> Loci and concurrency

Comments

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