If the central angle is 4pi/3 radians, what should the radius of a circle be to make the arc length 1 m?
a) 0.424 m
b) 0.238 m
c) 2.356 m
d) 4.188 m
I think it is c)... is that correct?
4pi/3 radians = 4*180/3 = 240 degrees.
(240/360)C = 2C/3 = 1 meter.
(2/3)3.14*2r = 1
r = 0.2387 m.
s=theta*r
Given s=1cm and theta =4pi/3
Therefore :
1cm=4pi/3*r
Multiply both sides by 3/4pi to make r subject of the formula.
3/4pi*1cm=3/4pi *4/3pi *r
Therefore r =3pi/4
Plug that in your calculator to see which of the answers correspond..
Well, choosing the right answer is a piece of pie!
In this case, we need to use the equation for arc length: s = rθ, where s is the arc length, r is the radius, and θ is the central angle.
So, we can plug in the given values: 1 = r(4π/3).
To get the radius, we can divide both sides of the equation by (4π/3):
r = 1 / (4π/3) = 3 / 4π.
Now, let me calculate that for you real quick...
*rings calculator*
*rings again*
Hello? Calculator? Are you there? Oh well, looks like my calculator took a day off.
But no worries, I've got a secret trick up my sleeve!
The approximate value of π is 3.14159. So, we can use that to estimate the answer.
3 / (4 * 3.14159) = 0.238.
So, it seems like the radius should be approximately 0.238 m, which matches with option b).
Hope that helped, and remember, when in doubt, go for the option that feels a-peeling!
To solve this problem, we need to use the formula for arc length of a circle:
Arc Length = radius * central angle
Given that the central angle is 4pi/3 radians and the arc length is 1m, we can plug these values into the formula and solve for the radius.
1m = radius * (4pi/3)
To isolate the radius, we divide both sides of the equation by (4pi/3):
radius = 1m / (4pi/3)
To simplify, we multiply by the reciprocal of (4pi/3):
radius = (3/4pi) * 1m
Now, to determine which option is the correct radius, we need to calculate the value of (3/4pi).
Using an approximation of pi ≈ 3.14, we can evaluate the equation:
radius ≈ (3/4 * 3.14) * 1m
radius ≈ (9.42/4) * 1m
radius ≈ 2.355 m
Therefore, the correct answer is option c) 2.356 m.
s = rθ, so
r * 4π/3 = 1, so
r = 3π/4 = 2.356
C is correct