Question

The sum of diameter of two circle is 35 cm
and the difference of their circumference is
66 cm. Find their radii.​

Answer 1

$\sf{\underline\blue{</p><p>\begin{gathered}if \: d1 = x \\ then \: d2 = 35 - x \\ r1 = x \div 2 \\ r2 =( 35 - x) \div 2 \\ cr1 = 2\pi \: r 1= \pi \: x \\ cr2 =2\pi \: r2 =2 (35 - x) \div 2 = 35\pi - x\pi \\ cr2 - cr1 = 22 \\ 35\pi - \pi \: x - \pi \: x = 22 \\ 35 - 2x\pi = 22 \\ 35 \times \frac{22}{7} - 2 \times \frac{22}{7} x = 22 \\ 110 - \frac{44}{7} x = 22 \\ 110 - 22 = \frac{44}{7} x \\ 88 \times \frac{7}{44} = x \\ x = 14 \: cm \\ therefore \: d1 = 14 \: and \: d2 = 21\\ hence \: the \: smaller \: area = \pi {r}^{2} \\ = \frac{22}{7} \times 7 \times 7 \\ = 154 {cm}^{2} \end{gathered} </p><p>ifd1=x</p><p>thend2=35−x</p><p>r1=x÷2</p><p>r2=(35−x)÷2</p><p>cr1=2πr1=πx</p><p>cr2=2πr2=2(35−x)÷2=35π−xπ</p><p>cr2−cr1=22</p><p>35π−πx−πx=22</p><p>35−2xπ=22</p><p>35× </p><p>7</p><p>22</p><p> </p><p> −2× </p><p>7</p><p>22</p><p> </p><p> x=22</p><p>110− </p><p>7</p><p>44</p><p> </p><p> x=22</p><p>110−22= </p><p>7</p><p>44</p><p> </p><p> x</p><p>88× </p><p>44</p><p>7</p><p> </p><p> =x</p><p>x=14cm</p><p>therefored1=14andd2=21</p><p>hencethesmallerarea=πr </p><p>2</p><p> </p><p>= </p><p>7</p><p>22</p><p> </p><p> ×7×7</p><p>=154cm </p><p>2</p><p> </p><p> </p><p> }}$

Answer 2

Hope you understand :)

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