← Back to topic
Vidaara.orgClass 10 · Mathematics
CodeVID-M10-10-SEC-01
Area of a Sector — Assignment
Chapter: Areas Related to Circles
Topic: Areas of Sector 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.
Area of a sector $=$
  • A.$\tfrac{\theta}{360^\circ}\pi r^2$
  • B.$\tfrac{\theta}{360^\circ}2\pi r$
  • C.$\pi r^2$
  • D.$\theta r^2$
2.
Length of an arc $=$
  • A.$\tfrac{\theta}{360^\circ}\pi r^2$
  • B.$\tfrac{\theta}{360^\circ}2\pi r$
  • C.$2\pi r$
  • D.$\pi r$
3.
A quadrant is a sector of angle:
  • A.$45^\circ$
  • B.$90^\circ$
  • C.$180^\circ$
  • D.$360^\circ$
4.
A semicircle is a sector of angle:
  • A.$90^\circ$
  • B.$180^\circ$
  • C.$270^\circ$
  • D.$360^\circ$
5.
The whole circle corresponds to $\theta=$
  • A.$90^\circ$
  • B.$180^\circ$
  • C.$360^\circ$
  • D.$270^\circ$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the area of a sector with $\theta=90^\circ,\ r=14$ ($\pi=\tfrac{22}{7}$).
7.
Find the arc length for $\theta=60^\circ,\ r=21$.
8.
Find the area of a quadrant of radius $7$.
9.
Find the sector area for $\theta=120^\circ,\ r=6$ ($\pi=3.14$).
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the area of a sector of angle $60^\circ$ in a circle of radius $6$ cm ($\pi=\tfrac{22}{7}$).
11.
Find the arc length of a $90^\circ$ sector of radius $14$ cm.
12.
A sector has area equal to $\tfrac16$ of a circle of radius $12$. Find its angle.
13.
Find the perimeter of a quadrant of radius $7$ cm.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A sector of a circle of radius $21$ cm has an angle of $120^\circ$. Find its area and arc length ($\pi=\tfrac{22}{7}$).
15.
The minute hand of a clock is $14$ cm long. Find the area it sweeps in $15$ minutes.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\tfrac{\theta}{360^\circ}\pi r^2$
  2. (B) $\tfrac{\theta}{360^\circ}2\pi r$
  3. (B) $90^\circ$
  4. (B) $180^\circ$
  5. (C) $360^\circ$
Section B — Short Answer (2 marks)
  1. $154$ cm$^2$.
  2. $22$ cm.
  3. $38.5$ cm$^2$.
  4. $37.68$ cm$^2$.
Section C — Short Answer (3 marks)
  1. $\tfrac{132}{7}\approx18.86$ cm$^2$.
  2. $22$ cm.
  3. $60^\circ$.
  4. $25$ cm.
Section D — Long Answer (5 marks)
  1. Area $462$ cm$^2$, arc $44$ cm.
  2. $154$ cm$^2$.
Generated by Vidaara.org · Assignment VID-M10-10-SEC-01 · vidaara.org