Vidaara.orgClass 10 · Mathematics
CodeVID-M10-10-CT
Areas Related to Circles — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- 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.
Circumference $=$
- A.$\pi r^2$
- B.$2\pi r$
- C.$\pi r$
- D.$\pi d^2$
2.
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.$\theta r^2$
3.
Minor segment area $=$
- A.sector $+$ triangle
- B.sector $-$ triangle
- C.circle $-$ sector
- D.triangle $-$ sector
4.
Area of a circle $=$
- A.$2\pi r$
- B.$\pi r^2$
- C.$\pi d$
- D.$\pi r$
5.
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.$\pi r$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the circumference for $r=14$ ($\pi=\tfrac{22}{7}$).
7.
Find the area of a sector with $\theta=90^\circ,\ r=14$ ($\pi=\tfrac{22}{7}$).
8.
State the formula for the area of a minor segment.
9.
Find the area for $r=7$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the area of a circle of diameter $28$ cm.
11.
Find the area of a sector of angle $60^\circ$ in a circle of radius $6$ cm ($\pi=\tfrac{22}{7}$).
12.
Find the area of the minor segment of a circle of radius $10$ cm with central angle $90^\circ$ ($\pi=3.14$).
13.
The circumference is $132$ cm; find the radius and area.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
The area of a circle is $154$ cm$^2$. Find its circumference.
15.
A sector of a circle of radius $21$ cm has an angle of $120^\circ$. Find its area and arc length ($\pi=\tfrac{22}{7}$).
Answer Key
Section A — Multiple Choice Questions
- (B) $2\pi r$
- (A) $\tfrac{\theta}{360^\circ}\pi r^2$
- (B) sector $-$ triangle
- (B) $\pi r^2$
- (B) $\tfrac{\theta}{360^\circ}2\pi r$
Section B — Short Answer (2 marks)
- $88$.
- $154$ cm$^2$.
- Sector area $-$ triangle area.
- $154$.
Section C — Short Answer (3 marks)
- $616$ cm$^2$.
- $\tfrac{132}{7}\approx18.86$ cm$^2$.
- $28.5$ cm$^2$.
- $r=21$ cm, area $1386$ cm$^2$.
Section D — Long Answer (5 marks)
- $44$ cm.
- Area $462$ cm$^2$, arc $44$ cm.
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