1. 11.2 Area of Sector & Population Density

2. How many squares are in the circle?
AREA
The area of a circle is the number of unit squares that can fit into the circle.
How many squares are in the circle?

3. Example: Find the Area of the Circle
2) Given the area of the circle,
find the radius.
A = 380 in2 r
380 = 𝜋𝑟2
380 𝜋 = 𝑟2
cm2
11.0 in ≈𝑟
cm2

4. SECTOR sector of a circle: part of the interior of a circle
bounded by two radii and an arc.
The size of a slice of pizza.

5. AREA OF A SECTOR = (fraction of the circle) X (area of circle)
The fraction of the circle multiplied by the area of the circle.
Area of a Sector
= (fraction of the circle) X (area of circle)
= x C
= x 𝜋r2

6. Examples: 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟= 𝑎 360 ∙𝐴 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟= 𝑎 360 ∙𝐴
1) 2)
72°
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟= 𝑎 360 ∙𝐴
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟= 𝑎 360 ∙𝐴
= ∙𝜋82
𝐴𝑟𝑒𝑎 𝑟𝑒𝑑 = ∙𝜋142
= 𝜋 𝑖𝑛2
= ∙𝜋 𝑓𝑡2
≈40.2 𝑖𝑛2
≈205.3 𝑓𝑡2

7. Example 3: The wall shown has a doorway cut out of it.
Jamie needs to paint the wall. Find, to the
nearest tenth of a foot, the area to be painted.
The area to be painted is a
rectangle – the entrance area.
The entrance can be divided
into a semi-circle and a square.
Area(paint) = A(rectangle) – [A(square + A(semi-circle)]
= 36∙ – (16∙ 𝜋∙82)
= 936 –(256+32𝜋)
≈579.5 𝑓𝑡 2

8. Population Density
The population density of a city, parish or state is a measure of how many people live within a given area.
Population density = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑙𝑎𝑛𝑑

9. Examples:
4) About 58,000 people live in a region with a 2 mile radius. Find the population density. 5) A region with a 3 mile radius has a population density of 1000 people per square mile. Find the number of people who live in the region.
Pop. density = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑙𝑎𝑛𝑑
≈ 58,000 4𝜋
about 4615 people per mi2
Pop. density = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑙𝑎𝑛𝑑
1000 = # 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 9𝜋
9000 𝜋 = # of people
about 28,274 people