Worksheet: Circular Segment

In this worksheet, we will practice finding the area of a circular segment.

Q1:

𝐴 𝐵 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:

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.

Q3:

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

Q4:

Which formula can be used to find the area of a circular segment, given a radius 𝑟 and a central angle 𝜃 ?

  • A 1 2 𝑟 ( 𝜃 + 𝜃 ) 2 r a d s i n
  • B 1 2 𝑟 ( 𝜃 𝜃 ) r a d s i n
  • C 2 𝑟 ( 𝜃 + 𝜃 ) r a d s i n
  • D 1 2 𝑟 ( 𝜃 𝜃 ) 2 r a d s i n
  • E 2 𝑟 ( 𝜃 𝜃 ) 2 r a d s i n

Q5:

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

  • A 1 2 𝑟 ( 𝜃 𝜃 ) 2 s i n
  • B 𝑟 ( 𝜃 𝜃 ) 2 s i n
  • C 2 𝜋 𝑟
  • D 𝜋 𝑟 2

Q6:

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 centimetre.

Q7:

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

Q8:

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.

Q9:

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.

Q10:

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.

Q11:

𝐴 𝐵 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 centimetre.

Q12:

A circle has a radius of 10 cm and the central angle of a circular segment is 2 5 𝜋 2 8 rad. Find the area of the circular segment giving the answer to two decimal places.

Q13:

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.

Q14:

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.

Q15:

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 centimetre.

Q16:

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 centimetre.

Q17:

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

Q18:

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 centimetre.

Q19:

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

Q20:

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.

Q21:

𝐴 is a point on the circumference of a circle, 𝐵 𝐶 is the diameter of the circle with length 21 cm and 𝑚 𝐴 𝐶 𝐵 = 5 4 . Find the area of the minor circular segment given by the chord 𝐴 𝐵 . Give the answer to two decimal places.

Q22:

𝐴 𝐵 𝐶 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 𝐵 𝐶 giving the answer to the nearest square centimetre.

Q23:

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.

Q24:

The radius of a circle 𝑀 is 17 cm. Points 𝐴 and 𝐵 lie on the circumference of a circle where the area of sector 𝐴 𝑀 𝐵 is 327 cm2. Find the area of the major circular segment of the chord 𝐴 𝐵 giving the answer to two decimal places.

Q25:

The height of a circular segment is 10 cm and the radius is 17 cm. Find the area of the circular segment giving the answer to the nearest square centimetre.

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