subtends 120 degrees. Give your answer in terms of π. Also, give a decimal approximation accurate to three places.
更新1:
is it 8 π/25.133
trigonometry homework help?
2020-09-11 12:40 pm
On a circle with radius of 12 inches find the area of the sector in square feet whose central angle
subtends 120 degrees. Give your answer in terms of π. Also, give a decimal approximation accurate to three places.
subtends 120 degrees. Give your answer in terms of π. Also, give a decimal approximation accurate to three places.
回答 (5)
2020-09-11 1:10 pm
Refer to the figure below.
Radius of the circle
= 12 in
= 1 ft
Area of the sector
= π × (1 ft)² × (120/360°)
= π/3 ft²
≈ 1.047 ft² (to 3 decimal places)
Radius of the circle
= 12 in
= 1 ft
Area of the sector
= π × (1 ft)² × (120/360°)
= π/3 ft²
≈ 1.047 ft² (to 3 decimal places)
2020-09-11 1:06 pm
Let me work through how you'd solve this.
Since the central angle is is 120°, you know that the area of the sector is one-third the area of the whole circle. (Because 120/360 = 1/3)
Since you know that the sector area is one-third the area of the circle, find the circle's area and divide by 3.
In this case, π×12²×(1/3) = 48π inches²
To square feet, that is π/3 feet²
And there's your answer.
This also works for any angle, not just 120°.
The area of the sector is θ/360° times the area of the circle. (Where θ is the angle) This makes sense if you think about it geometrically.
Hope this helps!
Since the central angle is is 120°, you know that the area of the sector is one-third the area of the whole circle. (Because 120/360 = 1/3)
Since you know that the sector area is one-third the area of the circle, find the circle's area and divide by 3.
In this case, π×12²×(1/3) = 48π inches²
To square feet, that is π/3 feet²
And there's your answer.
This also works for any angle, not just 120°.
The area of the sector is θ/360° times the area of the circle. (Where θ is the angle) This makes sense if you think about it geometrically.
Hope this helps!
參考: Math guy
2020-09-11 10:56 pm
The area of the sector=
0.5[(12/12)^2](120*pi/180*)=pi/3~1.047 ft^2
(correct to 3 d.p.)
Formula: Area of sector=(1/2)*(radius^2)*(angle in radians)
0.5[(12/12)^2](120*pi/180*)=pi/3~1.047 ft^2
(correct to 3 d.p.)
Formula: Area of sector=(1/2)*(radius^2)*(angle in radians)
2020-09-11 9:46 pm
It is: 1/3 times pi times 1^2 = 1/3pi or 1.047 square feet
2020-09-11 12:57 pm
Area of entire circle: pi*12^2 = 144*pi
Area of sector: (120/360)*144*pi = 48*pi =~ 150.796 ft^2
Area of sector: (120/360)*144*pi = 48*pi =~ 150.796 ft^2
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