Question

please answer by solving please ​

Answer 1

ANSWER:

Given:

• Ratio of circumferences of 2 circles = 3 : 5

To Find:

• Ratio of areas of the 2 circles.

Solution:

$\text{Let the 2 circles be C _1 and C _2 respectively.}\\\\\text{We are given that,}\\\\:\longrightarrow\sf{ Circumference_{C_1} : Circumference_{C_2} = 3 : 5}\\\\:\implies\sf{\dfrac{Circumference_{C_1}}{Circumference_{C_2}}=\dfrac{3}{5}}\\\\\text{We know that,}\\\\:\hookrightarrow \sf{Circumference=2\times\pi\times r}\\\\\text{So,}\\\\:\implies\sf{\dfrac{Circumference_{C_1}}{Circumference_{C_2}}=\dfrac{3}{5}}\\\\:\implies\sf{\dfrac{2\!\!\!/\,\times\pi\!\!\!/\,\times r_1}{2\!\!\!/\,\times\pi\!\!\!/\,\times r_2}=\dfrac{3}{5}}\\\\:\implies\sf{\dfrac{r_1}{r_2}=\dfrac{3}{5}- - - -(1)}$

$\text{We need to find,}\\\\:\longrightarrow\sf{Area_{C_1} : Area_{C_2}}\\\\:\implies\sf{\dfrac{Area_{C_1}}{Area_{C_2}}}\\\\\text{We know that,}\\\\:\hookrightarrow\sf{Area=\pi\times r^2}\\\\\text{So,}\\\\:\implies\sf{\dfrac{Area_{C_1}}{Area_{C_2}}}\\\\:\implies\sf{\dfrac{\pi\!\!\!/\,\times r_1^2}{\pi\!\!\!/\,\times r_2^2}}\\\\:\implies\sf{\dfrac{r_1^2}{r_2^2}}\\\\:\implies\sf{\left(\dfrac{r_1}{r_2}\right)^2}\\\\\text{From (1),}\\\\:\implies\sf{\left(\dfrac{r_1}{r_2}\right)^2}\\\\:\implies\sf{\left(\dfrac{3}{5}\right)^2}\\\\:\implies\sf{\dfrac{3^2}{5^2}}\\\\:\implies\sf{\dfrac{9}{25}}\\\\\bf{:\implies Area_{C_1} : Area_{C_2}=9:25}$

Formulae Used:

• Circumference of circle = 2πr
• Area of circle = πr²