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if length of AB/radius equal x/10 what is the ratio of the area of sector AOB to the area of the circle ?

User Mark Snyder
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1 Answer

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21 votes

\begin{gathered} (AB)/(r)=(x)/(10) \\ \text{Area of the circle is} \\ A=\pi r^2 \\ \text{Area of the circular sector is} \\ a=(AB\cdot r)/(2) \\ \text{Where AB is the arc-lenght} \\ \text{hence, the ratios is} \\ (a)/(A)=((AB\cdot r)/(2))/(\pi r^2) \\ (a)/(A)=(AB\cdot r)/(2\pi r^2) \\ (a)/(A)=\frac{AB}{2\pi\text{ r}} \end{gathered}
\begin{gathered} \text{SINCE} \\ (AB)/(r)=(x)/(10)\Rightarrow AB\questeq(r\cdot x)/(10) \\ \text{THEN,} \\ (a)/(A)=(r\cdot x)/((10)(2\pi r)) \\ (a)/(A)=(x)/((10)(2\pi)) \\ \text{hence,} \\ (a)/(A)=(x)/(20\pi) \end{gathered}

if length of AB/radius equal x/10 what is the ratio of the area of sector AOB to the-example-1
User Aderchox
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