Question

What are the sectors from least to greatest according to the area in square units

Answer 1

The sectors from least to greatest according to the area in square units are sector A < sector C < scetor B.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = π
`r^2` × θ/360

Where:

• r represents the radius of a circle.
• θ represents the central angle.

Note: The measure of an intercepted arc is equal to the central angle of a circle.

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = π
`r^2` × θ/360

Area of sector A = 3.14 ×
`2^2` × 169/360

Area of sector A = 5.896 sq. units.

Area of sector = π
`r^2` × θ/360

Area of sector B = 3.14 ×
`9^2` × 82/360

Area of sector B = 57.933 sq. units.

Area of sector = π
`r^2` × θ/360

Area of sector C = 3.14 ×
`6^2` × 117/360

Area of sector C = 36.738 sq. units.

Answer 2

The area of a sector is given by the formula:

`A_(sector)=(\theta)/(360)\pi r^2`

Then, we find the area for each sector.

Sector A

`A=(169)/(360)(3.14)(4)^2=(169)/(360)(3.14)(16)=23.6`

Sector B

`A=(82)/(360)(3.14)(9)^2=(41)/(180)(3.14)(81)=57.9`

Sector C

`A=(117)/(360)(3.14)(6)^2=(13)/(40)(3.14)(36)=36.7`

Answer:

Sector A < Sector C < Sector B