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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-10-SEG-01
Area of a Segment — Assignment
Chapter: Areas Related to Circles
Topic: Areas of Segment of a Circle
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Minor segment area $=$
  • A.sector $+$ triangle
  • B.sector $-$ triangle
  • C.circle $-$ sector
  • D.triangle $-$ sector
2.
Major segment area $=$
  • A.circle $-$ minor segment
  • B.sector $+$ triangle
  • C.circle $+$ sector
  • D.triangle
3.
A chord divides a circle into:
  • A.two sectors
  • B.two segments
  • C.two arcs
  • D.four parts
4.
For a semicircular segment, the triangle area is:
  • A.maximum
  • B.$0$
  • C.$\pi r^2$
  • D.$r^2$
5.
Segment area uses a sector and a:
  • A.square
  • B.triangle
  • C.rectangle
  • D.circle
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
State the formula for the area of a minor segment.
7.
If the sector area is $50$ and triangle area is $20$, find the minor segment area.
8.
If the circle area is $154$ and the minor segment is $14$, find the major segment.
9.
A $90^\circ$ sector of radius $10$ has a triangle of area:
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the area of the minor segment of a circle of radius $10$ cm with central angle $90^\circ$ ($\pi=3.14$).
11.
A chord subtends $60^\circ$ at the centre of a circle of radius $14$. Find the area of the corresponding minor sector.
12.
If a circle has area $314$ cm$^2$ and a minor segment of $28.5$ cm$^2$, find the major segment area.
13.
Find the sector area for a $90^\circ$ sector of radius $14$ cm ($\pi=\tfrac{22}{7}$).
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A chord of a circle of radius $14$ cm subtends a right angle at the centre. Find the area of the minor segment ($\pi=\tfrac{22}{7}$).
15.
A chord of a circle of radius $12$ cm subtends $120^\circ$ at the centre. Find the area of the minor segment ($\pi=3.14,\ \sqrt3=1.73$).

Answer Key

Section A — Multiple Choice Questions
  1. (B) sector $-$ triangle
  2. (A) circle $-$ minor segment
  3. (B) two segments
  4. (B) $0$
  5. (B) triangle
Section B — Short Answer (2 marks)
  1. Sector area $-$ triangle area.
  2. $30$.
  3. $140$.
  4. $50$.
Section C — Short Answer (3 marks)
  1. $28.5$ cm$^2$.
  2. $\tfrac{308}{3}\approx102.67$ cm$^2$.
  3. $285.5$ cm$^2$.
  4. $154$ cm$^2$.
Section D — Long Answer (5 marks)
  1. $56$ cm$^2$.
  2. $\approx88.44$ cm$^2$.
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