Find the radius of a circle in which a 40o central angle cuts off an arc whose length is 4pi

How to Determine the Length of an Arc dummies

circumference is pye times twice the radius or by the diameter
3.1417 X 6 ( diameter or 2 times the radius )= 18.8496
90 degrees is 1/4 of the circumference
18.8496 divided by 4 = 4.7124 cms
arc of 90 degrees =4.74124 cms

Assume the central angle is 35 degrees and the radius is 1.

The circumference of the whole circle is 2 x pi x radius. Since the radius is 1, the circumference will be 2 x pi.

Now a full circle is 360 degrees.

Now we can set up a ratio of 35 degrees is to 360 degree as x is to 2pi.

35 x
---- = -------
360 2xpi

Cross-multiply and isolate your variable.

Good luck.

Paul

The area of a circle is pi * r^^2.
For the first pond, the area is pi *14^^2. Let's say that is A
For the second pond the area is pi * r^^2. Let's say that is a.
But a = A/4 or, conversely 4a = A.
But A = pi*14^^2 = 4a = 4(pi * r^^2) or
pi*14^^2 = 4(pi*r^^2) or
pi*14^^2 = 4pi*r^^2 or
14^^2 = 4*r^^2
196 = 4*r^^2
196/4 = r^^2
49=r^^2
7=r
So a pond of radius 7m has an area a quarter of a circular pond of 14m.

About 146 and a half degrees.

If this is homework, make sure to show your work.

About 146 and a half degrees.

If this is homework, be sure to show your work.

Incomplete question.

You can not do it unless you know the measure of the central angle sustending (supporting) the arc. If the angle is known, you use the proportionality relation that follows:
If angle is in degrees
(length of arc) / circumference=(measure of central angle sustending arc)/360.
Here the circumference is 2*PI*radius.

If angle is in radians , the relation is somewhat simpler,
arc length= (radius length)* (angle measure in radians)
It is clear that in the last relation, the unit for the arc length is the same as the unit for the radius.

Hello and Welcome to FixYa!
Area of pizza (Combined Bread + Crust) = Area=pie * (radius)^2. If divided in 8 equal parts, Area of 1 piece=Area/8.
Area= 3.1415* (0.1524)^2 Area of 1 slice= Area/8 Concerned.

Hi,
The arc length can be obtained by:

(pi x r x Angle) / 180

or

(3.1415 x 5 x 30) / 180 = 2.618 in.

Hope this helps...