A circle has a radius of 6 ft.
What is the area of the sector formed by a central angle measuring 5π3 ?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
A circle has a radius of 12.6 cm.
What is the exact length of an arc formed by a central angle measuring 120°?
Enter your answer in the box. Express your answer using π .
CAN ANYONE PLEASE HELP?! I'M SICK, BUT I HAVE TO GET THESE CORRECT, PLEASE?!?
2017-02-28 11:05 pm
回答 (2)
2017-02-28 11:29 pm
PROBLEM 1:
First find the full area of the circle:
A = πr²
A = π6²
A = 36π
A full circle is 360° or 2π radians. I'm assuming your angle is actually 5π/3.
Take the full area an multiply it by the angle (5π/3 radians) divided by the full measure (2π radians).
36π * (5π/3) / 2π
= 18 * 5π/3
= 6 * 5π
= 30π
I'll leave it to you to calculate an approximation using π ≈ 3.14.
PROBLEM 2:
Again find the full area.
A = π12.6²
Then you need to multiply by the angle (120°) and divide by the full circle (360°).
So essentially you are taking 120/360 or 1/3 of the full area.
Again, I think you can calculate that:
(12.6)² * π / 3
First find the full area of the circle:
A = πr²
A = π6²
A = 36π
A full circle is 360° or 2π radians. I'm assuming your angle is actually 5π/3.
Take the full area an multiply it by the angle (5π/3 radians) divided by the full measure (2π radians).
36π * (5π/3) / 2π
= 18 * 5π/3
= 6 * 5π
= 30π
I'll leave it to you to calculate an approximation using π ≈ 3.14.
PROBLEM 2:
Again find the full area.
A = π12.6²
Then you need to multiply by the angle (120°) and divide by the full circle (360°).
So essentially you are taking 120/360 or 1/3 of the full area.
Again, I think you can calculate that:
(12.6)² * π / 3
2017-02-28 11:38 pm
1.
Area of circle = π r ² = 36 π ft²
Assuming that angle at centre is 5π/3
Area of sector = [ 5π/3 ] [ 36π ] / [ 2π ] ft²
Area of sector = [ 5π/3 ] [ 18 ] ft²
Area of sector = 30π ft²
Area of sector = 94•2 ft²
2.
Length of arc = [ 2π x 12•6 ] [ 1/3 ] cm2.
Length of arc = 8•6 π cm
Area of circle = π r ² = 36 π ft²
Assuming that angle at centre is 5π/3
Area of sector = [ 5π/3 ] [ 36π ] / [ 2π ] ft²
Area of sector = [ 5π/3 ] [ 18 ] ft²
Area of sector = 30π ft²
Area of sector = 94•2 ft²
2.
Length of arc = [ 2π x 12•6 ] [ 1/3 ] cm2.
Length of arc = 8•6 π cm
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