Class 10 Areas Related to Circles Mock Test (CBSE)

Topics in Areas Related to Circles

• Areas of sector and segment of a circle

Areas Related to Circles practice questions with answers

1. Q1Assertion and reason·1 mark
   Assertion (A): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is $2$ units. Reason (R): The area of a circle is $\pi r^2$ and its perimeter is $2\pi r$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer and step marks

   1. Correct option: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). Assertion calculation: $2\pi r = \pi r^2 \implies r = 2$, which is true. Reason states the correct formulas for area and perimeter, which directly explain the assertion.+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   Find the area of a sector of a circle with radius $6\text{ cm}$ if the angle of the sector is $60^\circ$. (Use $\pi = \frac{22}{7}$)

   1. (a)$\frac{132}{7}\text{ cm}^2$
   2. (b)$\frac{66}{7}\text{ cm}^2$
   3. (c)$\frac{132}{14}\text{ cm}^2$
   4. (d)$\frac{264}{7}\text{ cm}^2$
   Show answer and step marks

   1. Area = $\frac{60^\circ}{360^\circ} \times \frac{22}{7} \times 6^2 = \frac{132}{7}\text{ cm}^2$+1

   Answer: (a)
3. Q3Assertion and reason·1 mark
   Assertion (A): For a circle of radius $7\text{ cm}$, the area of the minor segment cut off by a chord that subtends $90^\circ$ at the centre is less than the area of the corresponding minor sector. Reason (R): The area of a sector of a circle is directly proportional to its central angle.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer and step marks

   1. Correct option: (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A). Sector area is $\frac{90}{360} \times \pi \times 7^2 = 38.5\text{ cm}^2$ and the triangle formed by the two radii and the chord has area $\frac{1}{2} \times 7 \times 7 = 24.5\text{ cm}^2$, so the segment is $14\text{ cm}^2$, which is less than $38.5\text{ cm}^2$. The reason is true, but it does not explain why the segment is smaller than the sector.+1

   Answer: (b)
4. Q4Multiple choice·1 mark
   The perimeter of a protractor is $72\text{ cm}$. Its diameter is: (Use $\pi = \frac{22}{7}$)

   1. (a)$14\text{ cm}$
   2. (b)$28\text{ cm}$
   3. (c)$36\text{ cm}$
   4. (d)$56\text{ cm}$
   Show answer and step marks

   1. Correct option: (b) $28\text{ cm}$. Perimeter = $\frac{18d}{7} = 72 \implies d = 28\text{ cm}$+1

   Answer: (b)
5. Q5Multiple choice·1 mark
   A sector of a circle of radius $14\text{ cm}$ subtends an angle of $45^\circ$ at the centre. Taking $\pi = \frac{22}{7}$, the area of the sector is:

   1. (a)$38.5\text{ cm}^2$
   2. (b)$154\text{ cm}^2$
   3. (c)$77\text{ cm}^2$
   4. (d)$308\text{ cm}^2$
   Show answer and step marks

   1. Correct option: (c) $77\text{ cm}^2$, since area of sector $=\frac{45}{360}\times\frac{22}{7}\times 14\times 14=\frac{1}{8}\times 616=77\text{ cm}^2$.+1

   Answer: (c)
6. Q6Assertion and reason·1 mark
   Assertion (A): If the area of a circle is $154\text{ cm}^2$, then its perimeter is $44\text{ cm}$ (take $\pi = \frac{22}{7}$). Reason (R): The perimeter (circumference) of a circle is given by the formula $2\pi r$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer and step marks

   1. Correct option: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). Both Assertion and Reason are true, and Reason correctly explains Assertion.+1

   Answer: (a)

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