Question

If the circumference of a circle and perimeter of a square are equal. Then ratio of their areas is​

Answer 1

Given :

The circumference of a circle and perimeter of a square are equal.

To find :

Ratio of their areas.

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Solution :

According to question,

$\star\;{\boxed{\sf{\purple{Circumference_{\;(circle)} = Perimeter_{\;(square)} }}}}$

$:\implies\sf 2\pi \: r = 4 \times a$⠀⠀⠀

$:\implies\sf \frac{\pi \: r}{2} = \: a$⠀

$:\implies\sf \frac{area \: of \: circle}{area \: of \: sqare} = \frac{\pi \: r}{ {a}^{2} }$⠀

$:\implies\sf \frac{\pi \: {r}^{2} }{\bigg({ \frac{\pi \: r}{2} }\bigg)^{2}}$⠀

$:\implies\sf \frac{\pi \: {r}^{2} }{ \frac{{\pi}^2\: {r}^2}{4} }$⠀

$:\implies\sf \frac{4}{\pi}$⠀

$:\implies\sf \frac{4 \times 7}{22}$⠀

$:\implies{\boxed{\sf{\pink{14\;:11}}}}\;\bigstar$

$\therefore\;{\underline{\sf{The\;required\;ratio\;will\;be\; \bf{14:11}.}}}$

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Answer 2

$\huge\boxed{\fcolorbox{purple}{ink}{Answer}}$

The formula unit mass of:

(i) ZnO = 65 u + 16 u = 81 u

(ii) Na2O = (23 u x 2) + 16 u = 46 u + 16 u = 62 u

(iii) K2C03 = (39 u x 2) + 12 u + 16 u x 3

= 78 u + 12 u + 48 u = 138 u