HS Math II
7.8 | Area of a Sector and Arc Length
Name: _________________________
Date: ____________ Per: _____
Topic: Circumference and Ratios
1. Four concentric circles are drawn below. Determine the exact circumference and area for each. Look for any
patterns .
Radius = 1
Radius = 2
Radius = 3
Radius = 4
Circumference
Area
A ratio is a comparison between two quantities and is generally written as a fraction. For example,
trigonometric ratios of sine, cosine, and tangent are ratios between the sides in a right triangle. We can make
ratios between any two quantities.
Write a ratio for the indicated quantities below.
2. The ratio of boys to girls in our math class.
3. The ratio of bathrooms to bedrooms in your house.
4. The ratio of boys to girls in your family.
5. The ratio of TVs to people that live in your house.
6. The ratio of people in your house to cell phones in your house.
Topic: Area of Sectors and Arc Length
Use what you know about finding circumference and area for circles to find the indicated distances below. You
may round all answers to the nearest tenth.
7. ⨀𝑅 is cut by two diameters; 𝑁𝑃 ⊥ 𝑂𝑄.
a. Find the distance to walk
̂.
along 𝑁𝑄
b. Find the area inside one of
the four sectors.
c. Find the distance to walk along the following path: Start at
P, then go to R, then to Q, over to N, then back to P.
8. ⨀𝑆 is cut by two diameters creating six congruent
central angles.
a. Find the distance to walk
̂.
along 𝑈𝑇
b. Find the area inside one of
the six sectors.
c. Find the distance to walk along the following path: Start at U,
then go to S, then to V, over to W, then to X, then back to U.
Use the given information to find the item(s) requested. (NOTE: EXACT below means to leave your answers
in terms of pi and, if necessary, as a fraction).
9. The exact area of a circle is 25π cm2. Find the
radius and the exact circumference of the circle.
r = _________________
10. The exact circumference of a circle is 10π feet.
Find the radius and the exact area of the circle.
C = _________________ r = _________________
A = _________________
11. The radius of the circle and the arc measure of
the small sector are given. Find the exact area of
the small sector.
12. The radius of the circle and arc measure of the
small sector are given. Find the exact arc length
between A and C.
Area of sector = _________________
̂ = _________________
𝐴𝐶
13. The exact area of the small sector below is 45π
yd2. Find the value of the radius of the circle.
̂ measures 26π mm.
14. The exact arc length of 𝐴𝐶
Find the value of the diameter of the circle.
r = _________________
d = _________________
̂ measures 30 m. What
15. The exact arc length of 𝐷𝐹
is the exact area of the circle?
16. The exact area of the small sector is π in2. What
is the circumference of the circle?
A = _________________
C = _________________