Area of the Sector

Area of the Sector

Mam Michelle M Villanueva

Multiple Choice

Calculate the area of the top circular part of the table that needs to be covered given that the side of the bottom square part of the table is 8 cm.

• $14\pi$

• $15\pi$

• $16\pi$

• $17\pi$

What's New

One of the true paradise of the Philippines is in Cebu City. Guimaras is famous for the world’s tastiest mangoes. A place known here for a snack is Pitstop located at Chavez building in San Miguel, Jordan. It is known for burger, pasta and PIZZA!

What's New

One of the famous pizza flavors Pitstop offers is the Mango Pizza which is a must-try for every tourist visiting Guimaras. The pizza crust was topped with thinly sliced ripe mangoes and then covered with cheese, drizzled with some crushed nuts and finished with sliced green pepper! Hmm… Yummy! 

Poll

Suppose that this pizza serves four people. You have eight people coming to your indoorhouse party. You’re only ordering one pizza but need to feed all eight. How do you divide that pizza equally? Would you double the radius? or would you double the sector angle?

What Is It

In Geometry, the area of a circle is  

 $A=\pi r^2$ where  $r$  is the radius of the circle. A sector of a circle is the region bounded by two radii of the circle and their intercepted arc. In the diagram below, sector ABC is bounded by  $\overline{AB}$ ,  $\overline{CB}$ and arc  $AC$ .

What Is It

The ratio of the area of a sector of a circle to the area of the whole circle  $\pi r^2$  is equal to the ratio of the measure of the intercepted arc to $360\degree$  .  

 $\frac{Area\ of\sec tor\ ABC}{πr^2}=\frac{measure\ ofarc\ AC}{360°}$  
 $Area\ of\sec tor\ ABC=\frac{measure\ of\ arc\ AC}{360°^{ }}\times\pi r^2$  

What Is It

In Figure 2, we see a whole circle while the Figure 3 illustrates part of a circle. Thus, the proportion  $\frac{Area\ of\ circle}{2π}=\frac{Area\ of\ \sec tor}{θ}$  

says that the ratio of area of the entire circle to the  $2\pi$  (1 revolution,  $\theta$ ) is equivalent to the ratio of area of the sector to the central angle  of the intercepted arc. 

What Is It

Through substitution, we say that  $\frac{(πr^2)}{2π}=\frac{A_{\sec tor}}{θ}$ . Notice that after simplifying, we now get the formula in finding the area of the sector which is 
 $A_{\sec tor}=\frac{1}{2}\times r^2θ$  

Multiple Choice

Example 1: 

A circle has a radius of 8 m. Find the area of the sector with central angle of 

 $\frac{\pi}{3}$  

•  $\frac{32\pi}{3}$  

•  $\frac{34\pi}{3}$  

•  $\frac{35\pi}{3}$  

•  $\frac{37\pi}{3}$  

Multiple Choice

Example 2:

A sector has a central angle  $\theta$ of  $13.3\degree$   with its area as  $133\ m^2$    Find the measure of the radius,  $r$  .

•  $33.75\ mm$  

•  $33.85\ mm$   

•  $33.95\ mm$  

•  $33.65\ mm$  

Multiple Choice

Example 3: 

A circle has a radius of

 $10$ 

Find the central angle  $\theta$   given that the area of the sector   $25\ in^2$  .

•  $\frac{1}{5}$  

•  $\frac{1}{4}$  

•  $\frac{1}{2}$  

•  $\frac{1}{3}$  

Multiple Choice

Practice 1

Find the area of the sector.

• $\frac{30\pi}{4}$

• $\frac{31\pi}{3}$
  

• $\frac{32\pi}{3}$
  

• $\frac{33\pi}{4}$
  

Multiple Choice

Practice 2

Find the area of the sector.

• $83\pi$
  

• $84\pi$
  

• $85\pi$
  

• $86\pi$

Multiple Choice

Practice 3

Find the area of the shaded region.

• $168.52$
  

• $168.25$

• $186.25$
  

• $186.52$
  

Multiple Choice

Practice 4

Find the area of the shaded region.

• 
  

  $540\pi$
  

• $541\pi$
  

• $542\pi$
  

• $543\pi$

Multiple Choice

Practice 5

Find the area of the shaded region.

• 
  

   $54\pi$  
  

•  $55\pi$  
  

•  $56\pi$  
  

•  $57\pi$  
  

Fill in the Blanks