Question

The diameter of two silver disc are in the ratio 2 ratio 3 what will the ratio of their areas?​

Answer 1

Answer:

4:9 ......

Step-by-step explanation:

ratio of diameter= ratio of radius

as area is directly proportional to square of radius so it is 4:9

Answer 2

$\star\small\sf\underline\blue{Given:-}$

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• The diameters of two silver discs are in the ratio 2:3.

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$\star\small\sf\underline\blue{Find \: Out:-}$

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• The ratio of their areas = ?

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$\star\small\sf\underline\blue{Solution:-}$

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• Ratio of diameter = 2:3

$\footnotesize\bold{\underline{\underline{\sf{\red{Let:-}}}}}$

• Diameter of first disc = 2x

$\sf \therefore$ Radius, $\sf{r_1}$ = $\sf\dfrac{2x}{2}$ = x

$\footnotesize\bold{\underline{\underline{\sf{\red{And:-}}}}}$

• Diameter of second disc = 3x

$\sf \therefore$ Radius, $\sf{r_2}$ = $\sf\dfrac{3x}{2}$

$\footnotesize\bold{\underline{\underline{\sf{\red{Now:-}}}}}$

$\sf \: Ratio \: of \: their \: areas = \dfrac{\pi \: r_1 \: ^2}{\pi r_2 \: ^2} \\ \\ \sf \: Ratio \: of \: their \: areas = \dfrac{ \cancel\pi \times (x) {}^{2} }{ \cancel\pi \times \bigg( \dfrac{3x}{2} \bigg) {}^{2} } \\ \\ \sf \: Ratio \: of \: their \: areas = \dfrac{ \cancel{x {}^{2} }}{ \dfrac{9 \: \: \cancel{x {}^{2}} }{4} } \\ \\ \sf \: Ratio \: of \: their \: areas = \dfrac{4}{9} \\ \\ \sf \: Ratio \: of \: their \: areas = \boxed{ \sf4 : 9}$

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$\star\small\sf\underline\blue{AnswEr:-}$

• The ratio of their areas is 4:9.