1. AREAS OF CIRCLES, SECTORS, SEGMENTS, AND ELLIPSES
Unit 27
AREAS OF CIRCLES, SECTORS, SEGMENTS, AND ELLIPSES

2. AREAS OF CIRCLES
The area of a circle is equal to the product of  and the square of the radius (A = r2)
The areas of two circles have the same ratio as the squares of the radii or diameters

3. AREAS OF CIRCLES
The areas of two circles are 144 mm2 and 36 mm2. Compare the radius of the larger circle with the radius of the smaller circle:
The radius of the larger circle is 2 times larger than the radius of the smaller circle

4. AREAS OF SECTORS
A sector of a circle is a figure formed by two radii and the arc intercepted by the radii
The area of a sector is given as:

5. AREAS OF SECTORS The area of a sector is given as:
Determine the area of a piece of pizza with a central angle of 48° and a radius of 10inches

6. AREAS OF SEGMENTS
A segment of a circle is a figure formed by an arc and the chord joining the end points of the arc
The area of a segment is found by subtracting the area of a triangle from the area of a sector
That triangle is always isosceles
2 radii for sides

7. AREAS OF SEGMENTS
Find the area of segment ACB in the figure below, given that AOB = 85, the radius of the circle is 4 in, and AB is 10 in:
Area of the sector: C B A O
2" 
A = (85°/360°)(4")2 = in2
Area of the triangle:
A = ½ bh = ½ (10")(2") = 10 in2
Area of the segment:
A = in2 – 10 in2 = in2 Ans

8. AREAS OF SEGMENTS
You build a nice deck in your rectangular back yard that is circular right outside the sliding doors. The yard is 50 ft long and 100 ft wide. The sides by the patio are 15 and 30 feet. The angle for the patio is 135° and the radius is 31.5 ft. Find the grass area in the yard.

9. AREAS OF SEGMENTS
You build a nice deck in your rectangular back yard that is circular right outside the sliding doors. The yard is 50 ft long and 100 ft wide. The sides by the patio are 15 and 30 feet. The angle for the patio is 135° and the radius is 31.5 ft. Find the grass area in the yard.
So the yard is 5000 square feet without a deck so what does the deck take out?

10. AREAS OF SEGMENTS
You build a nice deck in your rectangular back yard that is circular right outside the sliding doors. The yard is 50 ft long and 100 ft wide. The sides by the patio are 15 and 30 feet. The angle for the patio is 135° and the radius is 31.5 ft. Find the grass area in the yard.
So the area of the sector minus the area of triangle will give us the segment or the deck.
– = square feet
5000 – = square feet of grass remaining after the desk is installed

11. AREAS OF ELLIPSES
An ellipse is a closed oval-shaped curve that is symmetrical to two lines or axes that are perpendicular to each other
The longer axis is called the major axis and the shorter axis is called the minor axis
The area of an ellipse is equal to the product of  and one half the major axis and one half the minor axis

12. AREAS OF ELLIPSES
Find the surface area of an elliptical dining table that is 8 feet long (major axis) and 5 feet wide (minor axis):
Area = (8 ft  2)(5 ft  2)
= ft2 Ans

13. PRACTICE PROBLEMS
Find the area of a circle that has a radius of 7.25 meters.
Determine the radius of a circular patio which is to have an area of 14 square yards.
The radii of two circles are 6 inches and 2 inches. Compare the area of the larger circle with the area of the smaller circle.
Find the area of the sector of a circle with a central angle of 78° and a radius of 4.5 inches.

14. PRACTICE PROBLEMS (Cont)
Determine the central angle for a sector of a circle with a 3-meter radius given that the area of the sector is 3.77 square meters.
Find the area of a segment of a circle given a central angle of 60° and a radius of 4 inches when the height and base of the triangular section are 2 inches and 3 inches respectively.
Determine the area of an ellipse with a major axis of 7.5 cm and a minor axis of 5.5 cm.
Determine the major axis of an ellipse if its area is square yards and the minor axis is 12.3 yards.

15. PRACTICE PROBLEMS (Cont)
In a circular tank there is this cross sectional view and measurements. What is the area of the water in the bottom of the tank?

16. PROBLEM ANSWER KEY 165.13 m2 2.111 yards
The area of the larger circle is 9 times larger than the area of the smaller circle
in2
48°
5.378 in2
32.4 cm2
yards
17.39 yards2