Worksheet: Areas of Circular Segments

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 95. 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 120. Find the area of the segment giving the answer to two decimal places.

Q3:

What is the definition of a circular segment?

  • Aa region of a circle bounded by a chord and a central angle subtended by that arc
  • Ba region of a circle bounded between two chords and two arcs
  • Can arc which is half of the circumference
  • Da region of a circle bounded by two radii and an arc.
  • Ea region of a circle bounded by an arc and a chord passing through the end points of the arc.

Q4:

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

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

Q6:

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

Q7:

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.

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 centimeter.

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:

The chord and the radius of a circle both measure 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 155. Find the area of the major circular segment giving the answer to the nearest square centimeter.

Q12:

A circle has a radius of 10 cm and the central angle of a circular segment is 25𝜋28 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 segment giving the answer to the nearest square centimeter.

Q16:

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

Q17:

If 𝑀 is a circle whose radius is 68 cm, 𝑀𝐶𝐴𝐵, and 𝑀𝐶=35cm, 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 75. Find the radius of the circle giving the answer to the nearest centimeter.

Q19:

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.

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, 𝐵𝐶 is the diameter of the circle with length 21 cm and 𝑚𝐴𝐶𝐵=54. Find the area of the minor circular segment given by the chord 𝐴𝐵. 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 𝐵𝐶 giving the answer to the nearest square centimeter.

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 𝐴𝑀𝐵 is 327 cm2. Find the area of the major circular segment of the chord 𝐴𝐵 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 centimeter.

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