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Vidaara.orgClass 8 · Mathematics
CodeVID-M08-13-ARA-01
Area & Applications of Circles - Assignment
Chapter: Circles
Topic: Area and Applications of Circles
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.
The area of a circle is:
  • A.$2\pi r$
  • B.$\pi r^2$
  • C.$\pi d$
  • D.$\pi r$
2.
For $r=7$ ($\pi=\tfrac{22}{7}$), the area is:
  • A.$44$
  • B.$154$
  • C.$49$
  • D.$616$
3.
The area of a semicircle is:
  • A.$\pi r^2$
  • B.$\tfrac12\pi r^2$
  • C.$2\pi r^2$
  • D.$\tfrac14\pi r^2$
4.
Doubling the radius makes the area:
  • A.double
  • B.triple
  • C.four times
  • D.half
5.
Area is measured in:
  • A.units
  • B.square units
  • C.cubic units
  • D.degrees
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the area for $r=7$ ($\pi=\tfrac{22}{7}$).
7.
Find the area for $r=14$ ($\pi=\tfrac{22}{7}$).
8.
Find the area for $r=21$ ($\pi=\tfrac{22}{7}$).
9.
Find the area of a semicircle of radius $7$ ($\pi=\tfrac{22}{7}$).
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the area of a circle with diameter $28$ cm ($\pi=\tfrac{22}{7}$).
11.
The area of a circle is $154$ cm$^2$. Find its radius ($\pi=\tfrac{22}{7}$).
12.
Find the area of a quarter circle of radius $14$ ($\pi=\tfrac{22}{7}$).
13.
A circular garden has radius $35$ m. Find its area ($\pi=\tfrac{22}{7}$).
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A circular park has radius $21$ m. Find its area and the cost of grassing it at Rs $5$ per m$^2$ ($\pi=\tfrac{22}{7}$).
15.
From a square of side $14$ cm, the largest possible circle is cut out. Find the area of the remaining region ($\pi=\tfrac{22}{7}$).

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\pi r^2$
  2. (B) $154$
  3. (B) $\tfrac12\pi r^2$
  4. (C) four times
  5. (B) square units
Section B — Short Answer (2 marks)
  1. $154$.
  2. $616$.
  3. $1386$.
  4. $77$.
Section C — Short Answer (3 marks)
  1. $616$ cm$^2$.
  2. $7$ cm.
  3. $154$.
  4. $3850$ m$^2$.
Section D — Long Answer (5 marks)
  1. Area $1386$ m$^2$; cost Rs $6930$.
  2. $42$ cm$^2$.
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