Question

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

Answer 1

`\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}`