Q&A for How to Find Arc Length

To find the arc length, set up the formula Arc length = 2 x pi x radius x (arc's central angle/360), where the arc's central angle is measured in degrees.

If you're not given the central angle, you'll typically be given the sector area of the arc. To find the arc length with a sector area, multiply the sector area by 2. Then, divide the product by the radius squared ((SA*2)/r^2). Your answer gives you the central angle in radians. You now have the central angle in radians, so simply multiply the central angle by the radius to find the arc length.

That is correct. The vertex of an inscribed angle is on the outside of a circle. When an inscribed angle and a central angle share the same arc on a circle, the inscribed angle is equal to half of the measure of the central angle. The inscribed angle is also equal to half the measure of the arc.

If you know the arc length and central angle, just plug them into the above formula and solve for r. If the central angle is in degrees, use the formula arc length = 2*pi*r(θ/360). If the central angle is in radians, use the formula arc length = r*θ.

Some people like to convert pi to 3.14 and solve for the arc length's value, while others express the arc length in terms of pi. Just ask your teacher whether they want a decimal value for arc length or if it's okay to keep the arc length simplified in terms of pi.

It's the linear distance measured along the curve of an arc from one end to the other.

1 radian = 57.3°, so divide the central angle by 57.3° to get radians.

It's not possible. You need more information.

If the arc has a central angle of π/4, and the arc length is the radius multiplied by the central angle, then (3)(π/4) = 3π/4 = 2.36 m.

Multiply the square of the radius by pi and by the height (or length) of the cylinder.

An arc is a portion of the circumference of a circle. If you're asking about the full circumference of the tank, that would be 18.60 multiplied by pi.

Assuming the two arcs are part of the same circle, you would have to know the central angles of each arc. The ratio of the two arc lengths would be equal to the ratio of their respective central angles.

The arc length of a semicircle is half the circumference of the full circle. The circumference of a circle is πd, which in this case is 9π, or 28.26 units. That means the arc length of the semicircle is 14.13 units.

You would also need to know the arc length. Then use the arc length formula in Method 1 above, and work backwards to solve for the angle. Thus the central angle equals the arc length multiplied by 360°, then divided by 2πr.

If you're given the central angle in radians, multiply by 180° and divide by pi. That's equivalent to multiplying the angle in radians by 57.29°.

We can't.

You would also have to know the radius. The central angle equals the arc length multiplied by 180, divided by the product of pi and the radius. That is, [(180)(arc length)] / πr.

Multiply arc length by radius and divide by 2. It's similar to the area of a triangle because a thin wedge of circle approximates a triangle. You could also derive it from the pi r^2 formula for the area of a whole circle times the fraction of circle your arc represents (arc/2pir).

The formula relating arc length and central angle measure is arc length = θ(r) or r = arc length/θ.

If the radius and the chord are congruent, that means their lengths are the same. That means they form an equilateral triangle with the adjacent radius. That means the central angle for that chord is 60°, which is one-sixth of 360°. So the arc is one-sixth of the circle's circumference.

Work backwards. Your diameter is 75 inches so split it in half to get the radius which is 37.5. then use the first formula above to figure out the rest.

That wouldn't be enough information. You would need to know the central angle, too. Divide the central angle by 360°, multiply that number by 2π (6.28), and finally divide that product into the arc length. That gives you the radius.

You would also need to know the radius before you could find the arc length.

That means to include "π" when expressing the arc length. The expression is (2πr)(Ø/360°), where "Ø" is the central angle in degrees.

You would have to know the radius and the central angle of the sector. The formula is A = (πr²)(Ø/360°), where A is the sector's area, r is the circle's radius, and Ø is the sector's central angle in degrees.

The diameter is twice the radius = 30 feet. The circumference is pi times the diameter = 94.25 feet. The length of each arc is one-eighth of the circumference = 11.78 feet.

It can't be done. You have to know the central angle and the radius.

Yes, because all circles have a central angle of 360°.