Answer:
R= 12.
Step-by-step explanation:
First of all, let's sketch up this case to better understand what's going on. Check the attatched image below.
1. Finding a relative value.
How much is 20° or the whole circle?
Remember that a circle makes a total angle of 360°, therefore, 20°/360° is the percentage that this area of 8pi represent for this circle.
[tex]\frac{20}{360}= \frac{1}{18}[/tex] of the total circle.
Therefore, if we multiply the area A by this value of [tex]\frac{1}{18}[/tex], we get the current value that we have, 8pi.
2. Constructing an equation.
Taking the information from step 1, the area of 8pi is given by the next expression:
[tex]A*\frac{1}{18} =8\pi[/tex]
3. Rewrite the equation.
Remember that the formula for the area of a circle is the following:
[tex]A=\pi r^{2}[/tex]
We can now substitute the equation of step 2 and write:
[tex]\pi* r^{2}*\frac{1}{18} =8\pi[/tex]
4. Solve the equation for r.
[tex]\pi* r^{2}*\frac{1}{18} =8\pi\\\\r^{2}=\frac{8\pi}{\frac{1}{18} *\pi } \\\\r^{2}=\frac{8}{\frac{1}{18} } \\\\r^{2} =144\\\\r =\sqrt{144} \\\\r=12[/tex]
