Question

The ratio of the radii of two circle is 5:3. Find the ratio of their circumferences ​

Answer 1

Given : Ratio of the radii of the Circle is 5:3

To Find : Find the ratio of Circumference

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SolutioN :

$\dag \; {\underline{\underline{\pmb{\sf{ \; Let \; the \; Values \; :- }}}}}$

• Radii of 1st Circle = $\red{\sf{ 5y }}$
• Radii of 2nd Circle = $\red{\sf{ 3y }}$
• Circumference of 1st Circle = $\red{\sf{ C }}$
• Radii of 2nd Circle = $\red{\sf{ C' }}$

$\dag \; {\underline{\underline{\pmb{\sf{ \; Calculating \; the \; Ratio \; :- }}}}}$

$\begin{gathered} \; \; \; \red\longrightarrow \; \; {\pink{\sf{ Ratio = \dfrac{C}{C'} }}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{2 \times \pi \times r}{2 \times \pi \times r'} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{2 \times \pi \times 5y}{2 \times \pi \times 3y} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{ \pi \times 10y}{ \pi \times 6y} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{ \pi \times 10 \times y}{ \pi \times 6 \times y} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{ \cancel{\pi} \times 10 \times y}{ \cancel{\pi} \times 6 \times y} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{ 10 \times y}{ 6 \times y} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{ 10 \times \cancel{y} }{ 6 \times \cancel{y} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{ 10 }{ 6 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \cancel\dfrac{ 10 }{ 6 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; \sf{ Ratio = \dfrac{ 5 }{ 3 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longrightarrow \; \; {\underline{\boxed{\pmb{\purple{\frak{ Ratio = 5:3 }}}}}} \; \bigstar \\ \\ \\ \end{gathered}$

$\therefore \;$ Ratio of the Circumference is 5:3

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