Question

5. The diameters of two silver discs are in the ratio 2:3. What will be the ratio of their areas? ​

Answer 1

⭐Question :-

The diameters of two silver discs are in the ratio 2:3. What will be the ratio of their areas?

⭐Given :-

• Diameters of two silver discs are in ratio 2:3

⭐ To find :-

• Ratio of their areas.

⭐ Solution :-

Let the radii of the two disc be 2x and 3x.

★ Area of the first disc :

$\implies \tt{\pi{r}^{2} }$

★ Area of the second disc :

$\implies \tt{\pi {r}^{2} }$

★ Area of the two discs in ratio :-

$\implies \large \tt { \frac{\pi {(2x)}^{2}}{\pi(3x {)}^{2} } } \\ \\ \implies \large \tt{ \frac{ \frac{22}{7}(2x {)}^{2} }{ \frac{22}{7} (3x {)}^{2} } } \\ \\ \implies \large \tt{ \frac{ \cancel \frac{22}{7}(2x {)}^{2} }{ \cancel \frac{22}{7} (3x {)}^{2} } } \\ \\ \implies \large \tt { \frac{(2x {)}^{2} }{(3x {)}^{2} } } \\ \\ \implies \large \tt{ \frac{4 \: {\cancel{{x}^{2}}} }{9 \: \cancel{{x}^{2} }} } \\ \\ \implies \large \tt{ \frac{4}{9} } \\ \\ \implies \large \tt{4:9}$

Therefore, the area of the two discs in ratio 4:9

Joyful learning!!! ⛅