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In circle O the area of the sector with central angle AOB is 30 pi cm squared and radius OA is 6 cm. What is the angle measure of arc AB and the length of AB?
Wiki User
∙ 13y ago
The area of the whole circle is PI x 6 squared which equals 36 PI.
We can now use the ratio 30/36 = x/360 to find the angle (360 is the full angle if the circle, x is the angle of the segment, pi's cancell out)
If we solve for x we get 300 degrees which is the angle we need.
As for the length, the circles circumference is 12 PI (12 is the diameter).
This means that 30/36= AB/12PI
AB=10PI
Wiki User
∙ 13y ago
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How do you find the arc length with the angle given?
An arc can be measured either in degree or in unit length. An arc is a portion of the circumference of the circle which is determined by the size of its corresponding central angle. We create a proportion that compares the arc to the whole circle first in degree measure and then in unit length. (measure of central angle/360 degrees) = (arc length/circumference) arc length = (measure of central angle/360 degrees)(circumference) But, maybe the angle that determines the arc in your problem is not a central angle. In such a case, find the arc measure in degree, and then write the proportion to find the arc length.
What is the length of an arc of a circle?
The length of an arc of a circle refers to the product of the central angle and the radius of the circle.
What is the formula of a central angle of a circle?
Central angle of a circle is the same as the measure of the intercepted arc. davids1: more importantly the formulae for a central angle is π=pi, R=radius Central Angle= Arc Length x 180 / π x R
What is the measure of the arc of a circle intercepted by a central angle that measures 64 degrees?
64°/360° = 8/45 of the circle = 0.1777 (rounded, repeating)The arc's length is 8/45 of the circle's total circumference.
How do you work out the circumference of a circle using radius?
The formula for calculating the circumference of a circle is 2πr, where r is the radius of the circle and π is 3.1415926535890793 - usually shorted to either 3.1416 or 3.14 So that the circumference of a circle with a radius of 10 units is 62.83 units There are pi radians in a half of a circle. Thus, the measure of a central angle which is a straight line is pi radians. We have a formula that show that the length of an intercepted arc is equal to the product of the angle in radians that intercepts that arc, with the length of the radius of the circle. So we can say that the length of a semicircle is (pi)(r). In a full circle are 2pi radians. So the length of intercepted arc from a central angle with measure 2pi is 2(pi)(r).
How do you find the degree measure of a central angle in a circle if both the radius and the length of the intercepted arc are known?
-- Circumference of the circle = (pi) x (radius) -- length of the intercepted arc/circumference = degree measure of the central angle/360 degrees
Do squared meters measure length?
No. A metre measures length, a squared metre measures area.
How do you find the arc length with the angle given?
An arc can be measured either in degree or in unit length. An arc is a portion of the circumference of the circle which is determined by the size of its corresponding central angle. We create a proportion that compares the arc to the whole circle first in degree measure and then in unit length. (measure of central angle/360 degrees) = (arc length/circumference) arc length = (measure of central angle/360 degrees)(circumference) But, maybe the angle that determines the arc in your problem is not a central angle. In such a case, find the arc measure in degree, and then write the proportion to find the arc length.
What is the length of an arc of a circle?
The length of an arc of a circle refers to the product of the central angle and the radius of the circle.
How do you measure an area squared?
Areas are already of the type that are measured in squared units of length.
What is the formula of a central angle of a circle?
Central angle of a circle is the same as the measure of the intercepted arc. davids1: more importantly the formulae for a central angle is π=pi, R=radius Central Angle= Arc Length x 180 / π x R
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The area of a circle is equal to that of a triangle whose base has the length of the circle's circumference (distance around the circle) and whose height equals the circle's radius which comes to Pi multiplied by the radius squared. Area of Triangle 1/2 *base*height
What is the measure of the arc of a circle intercepted by a central angle that measures 64 degrees?
64°/360° = 8/45 of the circle = 0.1777 (rounded, repeating)The arc's length is 8/45 of the circle's total circumference.
A line segment that connects the center of a circle to a point on the circle?
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How do you work out the circumference of a circle using radius?
The formula for calculating the circumference of a circle is 2πr, where r is the radius of the circle and π is 3.1415926535890793 - usually shorted to either 3.1416 or 3.14 So that the circumference of a circle with a radius of 10 units is 62.83 units There are pi radians in a half of a circle. Thus, the measure of a central angle which is a straight line is pi radians. We have a formula that show that the length of an intercepted arc is equal to the product of the angle in radians that intercepts that arc, with the length of the radius of the circle. So we can say that the length of a semicircle is (pi)(r). In a full circle are 2pi radians. So the length of intercepted arc from a central angle with measure 2pi is 2(pi)(r).
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It is 10/18 = 0.55... radians.
What does the diameter of a circle measure?
The length across the circle. 2 x the radius.
