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Worksheet: Circular Segment

Q1:

𝐴 𝐡 is a chord of length 55 cm with a central angle of 9 5 ∘ . Find the area of the minor circular segment giving the answer to one decimal place.

Q2:

A circle has a radius of 10 cm. A chord is drawn of length 14 cm. Find the area of the major segment giving the answer to the nearest square centimeter.

  • A 573 cm2
  • B 187 cm2
  • C 1 146 cm2
  • D 287 cm2

Q3:

A circle has a radius of 30 cm. A chord is drawn of length 47 cm. Find the area of the major segment giving the answer to the nearest square centimeter.

  • A 4 911 cm2
  • B 1 579 cm2
  • C 9 823 cm2
  • D 2 456 cm2

Q4:

A chord of length 90 cm is 42 cm away from the center of its circle. Find the area of the minor circular segment giving the answer to the nearest square centimeter.

  • A 4 996 cm2
  • B 2 433 cm2
  • C 38 cm2
  • D 1 216 cm2
  • E 2 976 cm2

Q5:

The length of a chord is 43 cm and the radius of the circle is 26 cm. Find the area of the circular segment giving the answer to the nearest square centimetre.

Q6:

A chord and radius of a circle is 33 cm. Find the area of the major circular segment giving the answer to two decimal places.

Q7:

Which formula can be used to find the area of a circular segment, given a radius π‘Ÿ and a central angle πœƒ ?

  • A 1 2 π‘Ÿ ( πœƒ + πœƒ ) 2 r a d s i n
  • B 1 2 π‘Ÿ ( πœƒ βˆ’ πœƒ ) r a d s i n
  • C 2 π‘Ÿ ( πœƒ + πœƒ ) r a d s i n
  • D 1 2 π‘Ÿ ( πœƒ βˆ’ πœƒ ) 2 r a d s i n
  • E 2 π‘Ÿ ( πœƒ βˆ’ πœƒ ) 2 r a d s i n

Q8:

The area of a circular sector is 1 001 cm2 and the arc length is 91 cm. The central angle of a circular segment is half the central angle of the circular sector. Find the area of the circular segment giving the answer to two decimal places.

Q9:

𝐴 is a point on the circumference of a circle, 𝐡 𝐢 is the diameter of the circle with length 21 cm and π‘š ∠ 𝐴 𝐢 𝐡 = 5 4 ∘ . Find the area of the minor circular segment given by the chord 𝐴 𝐡 . Give the answer to two decimal places.

Q10:

A chord and radius of a circle is 24 cm. Find the area of the minor circular segment giving the answer to two decimal places.

Q11:

𝐴 𝐡 𝐢 is an equilateral triangle inscribed in a circle where the side length is 22 cm. Find the area of the minor circular segment with chord 𝐡 𝐢 giving the answer to the nearest square centimeter.

  • A 50 cm2
  • B 198 cm2
  • C 8 cm2
  • D 99 cm2
  • E 239 cm2

Q12:

A circle has a radius of 10 cm and the central angle of a circular segment is rad. Find the area of the circular segment giving the answer to two decimal places.

Q13:

The radius of a circle is 40 cm and the arc length of a segment is 18 cm. Find the area of the segment giving the answer to two decimal places.

Q14:

The diameter of a circle is 14 cm and the central angle is 5.79 rad . Find the area of the circular segment giving the answer to two decimal places.

Q15:

𝐴 𝐡 is a chord of length 17 cm with a central angle of 1 5 5 ∘ . Find the area of the major circular segment giving the answer to the nearest square centimeter.

  • A 76 cm2
  • B 303 cm2
  • C 163 cm2
  • D 152 cm2

Q16:

The radius of two congruent circles is 89 cm and each circle passes through the center of the other. Find the area of their common region giving the answer to the nearest square centimeter.

  • A 4 865 cm2
  • B 11 725 cm2
  • C 55 cm2
  • D 9 730 cm2
  • E 23 449 cm2

Q17:

The radius of two congruent circles is 7 cm and each circle passes through the center of the other. Find the area of their common region giving the answer to the nearest square centimeter.

  • A 30 cm2
  • B 73 cm2
  • C 4 cm2
  • D 60 cm2
  • E 145 cm2

Q18:

The chord length of a circular segment is 15 cm and the height is 6 cm. Find the area of the circular sengment giving the answer to the nearest square centimeter.

  • A 81 cm2
  • B 78 cm2
  • C 157 cm2
  • D 67 cm2
  • E 10 cm2

Q19:

What is the total area of the minor and major circular segments of the same circle?

  • A 1 2 π‘Ÿ ( πœƒ βˆ’ πœƒ ) 2 s i n
  • B π‘Ÿ ( πœƒ βˆ’ πœƒ ) 2 s i n
  • C 2 πœ‹ π‘Ÿ
  • D πœ‹ π‘Ÿ 2

Q20:

What is the definition of a circular segment?

  • A a region of a circle bounded by a chord and a central angle subtended by that arc
  • B a region of a circle bounded by two radii and an arc.
  • C a region of a circle bounded between two chords and two arcs
  • D a region of a circle bounded by an arc and a chord passing through the end points of the arc.
  • E an arc which is half of the circumference

Q21:

A circular flower bed is divided into four parts by an equilateral triangle inscribed in the circle. The radius of the flower bed is 9 m. Find the area of each minor circular segment giving the answer to two decimal places.

Q22:

Find the area of the minor segment with chord of length 24 cm and a height of 8 cm. Give the answer to the nearest square centimeter.

  • A 277 cm2
  • B 258 cm2
  • C 11 cm2
  • D 139 cm2

Q23:

The area of a circular segment is 34 cm2 and the central angle is 7 5 ∘ . Find the radius of the circle giving the answer to the nearest centimeter.

  • A 5 cm
  • B 7 cm
  • C 10 cm
  • D 14 cm

Q24:

If 𝑀 is a circle whose radius is 68 cm, 𝑀 𝐢 βŸ‚ 𝐴 𝐡 , and 𝑀 𝐢 = 3 5 c m , find the area of the minor circular segment rounded to the nearest three decimal places.

Q25:

The area of a circle is 227 cm2 and the central angle of a segment is 1 2 0 ∘ . Find the area of the segment giving the answer to two decimal places.