Circular segment - math word problems

a circular segment is a region of a circle which is "cut off" from the rest of the circle by a secant or a chord.

  1. Tunnel boring
    tunnel How much material did they dig when cutting the 400m long tunnel? The content of the circular segment, which is the cross section of the tunnel is 62m2.
  2. Chord BC
    tetiva2 A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
  3. Circular segment
    odsek Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
  4. Circular pool
    arc_open The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  5. Spherical segment
    circular_segment_1 Spherical segment with height h=5 has a volume V=117. Calculate the radius of the sphere of which is cut this segment.
  6. Arc and segment
    odsek_kruh Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 11 and corresponding angle is ?.

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