5 points to explain how to do the problem?
2012-12-31 4:46 pm
If George wants to plant a border of bushes in the shape of an arc along the edge of a circular walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures 1.5 radians, what is the length of the border?
回答 (3)
2012-12-31 4:57 pm
You should KNOW
1. The circumference of a circle is C = 2πr
2. A circle has 360° or 2π radians.
Given these two simple facts, which you should know cold, determining what fraction of a complete circle 1.5 rad is, is a trivial 4th grade arithmetic problem. Knowing how to convert that fraction of the circle to the fraction of its circumference is also a trivial 4th grade arithmetic problem.
Questions?
......
1.5 ÷ (2*π) = 1.5 ÷ (2 * 3.1415) = 1.5 ÷ 6.283 = arc length/Circumfrence = Q
-=-
C = 2πr = 2*3.1415*5 yds = 6.283*5 yds = 31.415 yds
Q * 31.215 = arc length in yds.
-=-=-
There is nothing wrong with knowing the formula for arc length given the radius, the problem with it is that you won't use it very often and you will tend to forget whether it is in radians or degrees and whether it is radius or diameter. Being able to derive it from some basic facts you must learn anyway is the way I believe is actually easier. Oh, yeah, you need to know pi, π = 3.1415 (approximately)
1. The circumference of a circle is C = 2πr
2. A circle has 360° or 2π radians.
Given these two simple facts, which you should know cold, determining what fraction of a complete circle 1.5 rad is, is a trivial 4th grade arithmetic problem. Knowing how to convert that fraction of the circle to the fraction of its circumference is also a trivial 4th grade arithmetic problem.
Questions?
......
1.5 ÷ (2*π) = 1.5 ÷ (2 * 3.1415) = 1.5 ÷ 6.283 = arc length/Circumfrence = Q
-=-
C = 2πr = 2*3.1415*5 yds = 6.283*5 yds = 31.415 yds
Q * 31.215 = arc length in yds.
-=-=-
There is nothing wrong with knowing the formula for arc length given the radius, the problem with it is that you won't use it very often and you will tend to forget whether it is in radians or degrees and whether it is radius or diameter. Being able to derive it from some basic facts you must learn anyway is the way I believe is actually easier. Oh, yeah, you need to know pi, π = 3.1415 (approximately)
2012-12-31 5:02 pm
use the formula for length of an arc
l = 2r + (@ / 360) x 2 pi r
l = 2r + (@ / 360) x 2 pi r
2012-12-31 4:52 pm
r = 5
θ = 1.5 rad
1.5/(2π) * 2π(5)
= 7.5 yards
Therefore, the border is 7.5 yards long.
θ = 1.5 rad
1.5/(2π) * 2π(5)
= 7.5 yards
Therefore, the border is 7.5 yards long.
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