Question

4 part question: Circle C has a diameter of 10 inches and is divided into 10 congruent sectors.

1. Find the measure of the arc that bounds each sector.
2.Use your answer from part 1 to find the fraction of the circle that each sector covers.
3.what is the area of circle C?
4.use your results from parts 1,2 and 3 to find the area of each sector in circle C.

Answer 1

I will draw the circle...give me a bit.

Answer 2

1. If d=10 then r=5. The length of circle C = 2pi*r = 10pi
So one arcs length is:\[\frac{ 10\pi }{ 10 }=\pi \] or\[\frac{ 360^{o} }{ 10 }=36^{o} \]

Answer 3

2. Each sector covers 1/10 of the circle.
3. Area of the circle is S = pi*r^2, then\[S=\pi*r ^{2}=5^{2}\pi=25\pi \] square units.

Answer 4

4. Each sector covers 1/10 of the circle which means it covers\[S _{s}=\frac{ S }{ 10 }=\frac{ 25\pi }{ 10 }=2.5\pi\] square units.