Central angle

What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?

Correct answer:

x =  24.0855 cm

Step-by-step explanation:

$$\begin{gathered} D=46\text{ cm } \\ \alpha =30^{\circ }\to \text{ rad}=30^{\circ }\cdot {\displaystyle \frac{\pi }{180}}=30^{\circ }\cdot {\displaystyle \frac{3.1415926}{180}}=0.5236=\pi \mathrm{/}6 \\ x=D\cdot \alpha =46\cdot 0.5236=24.0855\text{ cm} \end{gathered}$$

Try another example

Related math problems and questions:

• Length of the arc
  What is the length of the arc of a circle k (S, r=68mm), which belongs to a central angle of 78°?
• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• The central
  The central angle of a sector is 30° and the radius is 15 m. Determine its perimeter.
• Circular arc
  Calculate the length of the circular arc if the diameter d = 20cm and the angle alpha = 142 °
• Circle arc
  Calculate the circular arc area in m² where the diameter is 263 dm, and a central angle is 40°. Result round to three decimal places.
• The length
  The length of the circle is 24 cm. What is the length of the circular arc of the corresponding angle 30°?
• Minute hand
  What is the distance the minute hand of the clock travels in 12 minutes, if the diameter of the clock is 30 cm and the hand extends to a distance of 2 cm from the edge of the clock?
• Arc
  Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
• Arc
  What area of a circle occupied the flowers planted in the arc of a circle with radius 3 m with central angle 45°?
• Pulley
  On wheels with a diameter of 40 cm is fixed rope with the load. Calculate how far is load lifted when the wheel turns 7 times?
• Track arc
  Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?
• Base
  Base of building is circle with diameter 25 m. Calculate the circumference of a circular trench witch diameter is 41 cm wider than the diameter of the base.
• Gamma angle
  Find the magnitude of the gamma angle in triangle ABC if: α = 38° 56 ’and β = 47° 54’.
• Aircraft bearing
  Two aircraft will depart from the airport at the same time, the first with a course of 30° and the second with a course of 86°. Both fly at 330 km/h. How far apart will they be in 45 minutes of flight?
• Inner angles
  The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
• Clocks
  What distance will describe the tip of minute hand 6 cm long for 20 minutes when we know the starting position with finally enclose hands each other 120°?
• Arc
  The length of the circle is 41 amd arc length of the circle 9. What is the magnitude of the angle of this arc?