Step by step
The question
Question: find the arc length s of a circle with radius 8 m and angle 3π/2.
The arc is the curved part of the edge.
We know the radius: r = 8 m.
And the angle: θ = 3π/2.
1 Write the rule
The rule for the arc length: s = rθ.
θ must be in radians.
Why?
A full turn is 2π.
Then s is 2π times r: the whole edge of the circle.
A smaller angle gives a part of it.
Careful!
The rule only works with the angle in radians.
Ours already is.
2 Put the numbers in
Now put the numbers in: r = 8 and θ = 3π/2.
3 Work it out
8 times 3π is 24π.
The bottom stays 2.
24 and 2 can both be divided by 2.
24 ÷ 2 is 12.
2 ÷ 2 is 1.
So s = 12π m.
That is the exact answer.
With the calculator, π is about 3.14159.
So s is about 37.70 m, to the nearest hundredth.
4 Check
Let's check another way.
3π/2 is a part of the full turn, 2π: 3/4 of it.
The whole edge is 2π r: 16π.
3/4 of 16π is 12π.
The same answer!
So it is right.
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: work it out.
Last: check.