Information
You have already completed the quiz before. Hence you can not start it again.
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
-
Question 1 of 4
Find the area of the shaded region
Use π=3.1415
Round your answer to two decimal places
Incorrect
Loaded: 0%
Progress: 0%
0:00
Area of a Sector
A=12r2θ
Converting Degrees to Radian
radian=degrees×π180°
First, convert the degree into radian
radian |
= |
degrees×π180° |
|
|
= |
75°×π180° |
|
|
= |
75°π180° |
|
|
= |
5π12 |
Simplify |
Next, substitute the known values and solve for angle of the shaded region
A |
= |
12r2θ |
|
|
= |
12⋅62⋅5π12 |
Substitute known values |
|
|
= |
12⋅36⋅15.707512 |
Use π=3.1415 |
|
|
= |
18⋅1.3089 |
|
= |
23.56 |
Rounded to two decimal places |
-
Question 2 of 4
Find the area of the shaded region
Use π=3.14159
Round your answer to two decimal places
Incorrect
Loaded: 0%
Progress: 0%
0:00
Area of a Sector
A=12r2θ
Converting Degrees to Radian
radian=degrees×π180°
First, convert the degree into radian
radian |
= |
degrees×π180° |
|
|
= |
150°×π180° |
|
|
= |
150°π180° |
|
|
= |
5π6 |
Simplify |
Next, find the radius of the smaller sector by subtracting the radius of the larger sector to the total radius
radius(Smaller sector) |
= |
40−26 |
|
= |
14 |
Then, substitute the known values and solve for angle of the whole sector
r |
= |
40 |
|
θ |
= |
5π12 |
Area(Whole sector) |
= |
12r2θ |
|
|
= |
12⋅402⋅5π6 |
Substitute known values |
|
|
= |
12⋅1600⋅5π6 |
Evaluate |
|
|
= |
20003⋅π |
Simplify |
|
|
= |
2094.39 |
Rounded to two decimal places |
Next, substitute the known values and solve for angle of the smaller sector
r |
= |
14 |
|
θ |
= |
5π12 |
Area(Smaller sector) |
= |
12r2θ |
|
|
= |
12⋅142⋅5π6 |
Substitute known values |
|
|
= |
12⋅196⋅5π6 |
Evaluate |
|
|
= |
98⋅56⋅π |
Simplify |
|
|
= |
81.667×π |
|
|
= |
256.56 |
Rounded to two decimal places |
Finally, subtract the area of the smaller sector from the area of the whole sector to get the area of the shaded region
Area(Shaded Region) |
= |
Area(Whole sector)−Area(Smaller sector) |
|
= |
2094.39−256.56 |
|
= |
1837.83 |
A=1837.83 cm2
-
Question 3 of 4
Find the area of the purple shaded region
Incorrect
Loaded: 0%
Progress: 0%
0:00
Area of a Sector
A=12r2θ
Converting Degrees to Radian
radian=degrees×π180°
First, convert the degree into radian
radian |
= |
degrees×π180° |
|
|
= |
60°×π180° |
|
|
= |
60°π180° |
|
|
= |
π3 |
Simplify |
Next, substitute the known values and solve for angle of the whole sector
Area(Whole sector) |
= |
12r2θ |
|
|
= |
12⋅702⋅π3 |
Substitute known values |
|
|
= |
2450π3 |
Simplify |
Next, substitute the known values and solve for angle of the smaller sector
Area(Smaller sector) |
= |
12r2θ |
|
|
= |
12⋅502⋅π3 |
Substitute known values |
|
|
= |
1250π3 |
Simplify |
Finally, subtract the area of the smaller sector from the area of the whole sector to get the area of the shaded region
Area(Shaded Region) |
= |
Area(Whole sector)−Area(Smaller sector) |
|
|
= |
2450π3−1250π3 |
|
|
= |
1200π3 |
|
|
= |
400π |
Simplify |
-
Question 4 of 4
Find the area of the shaded region
Use π=3.14
Round your answer to three decimal places
Incorrect
Loaded: 0%
Progress: 0%
0:00
Area of a Segment
A=12r2(θ−sinθ)
Converting Degrees to Radian
radian=degrees×π180°
First, convert the degree into radian
radian |
= |
degrees×π180° |
|
|
= |
45°×π180° |
|
|
= |
45°π180° |
|
|
= |
π4 |
Simplify |
Next, substitute the known values and solve for angle of the shaded region
A |
= |
12r2(θ−sinθ) |
|
|
= |
12⋅122⋅(π4−sinπ4) |
Substitute known values |
|
|
= |
12⋅144⋅(π4−1√2) |
|
|
= |
72⋅(0.785−0.7071) |
Use π=3.14 |
|
= |
72⋅0.0783 |
|
= |
5.637 |
Rounded to three decimal places |