1. What is the area of a circle with a diameter of 14 cm? (Take pi = )
- A154 cm²
- B196 cm²
- C88 cm²
- D308 cm²
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Answer: A) 154 cm²
The radius is half the diameter, so r = 7 cm. The area is pi * 7² = 49 * = 154 cm².
Class 10 Areas Related to Circles — practice questions with answers
Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the minor segment. (Take pi = 3.14)
- A31.5
- B57
- C25.5
- D28.5
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Answer: D) 28.5
Sector area = *3.14*10² = 78.5 cm². Triangle area = *10*10 = 50 cm². Minor segment = 78.5 - 50 = 28.5 cm².
3. The areas of two sectors of two different circles are equal. Their central angles are 60° and 40°. Which sector has the larger radius?
- AThe sector with the 60° angle
- BThe sector with the 40° angle
- CBoth have equal radius
- DCannot be determined
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Answer: B) The sector with the 40° angle
Equal areas: *pi*r1² = *pi*r2², so 60*r1² = 40*r2², giving r2² = 1.5*r1². Hence r2 > r1, so the smaller-angle (40°) sector has the larger radius.
4. A sector of radius 3.5 cm is drawn at each of the three vertices of a triangle, each sector lying inside the triangle. Find the total area of the three sectors. (Take pi = )
- A38.5 cm²
- B9.63 cm²
- C28.88 cm²
- D19.25 cm²
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Answer: D) 19.25 cm²
You never need the individual angles. The three angles of a triangle add up to 180°, and all three sectors have the same radius, so together they make a sector of angle 180°, i.e. a semicircle. Total = * * 3.5² = * 38.5 = 19.25 cm². Answering 38.5 assumes the angles add to 360°, and 28.88 assumes 270°.
5. Which is bigger: a 60° sector of a circle of radius 12 cm, or a 120° sector of a circle of radius 8 cm? (Take pi = 3.14)
- AThe 120° sector, by about 8.4 cm²
- BThe 60° sector, by about 8.4 cm²
- CThey have equal areas
- DThe 60° sector, by about 251.2 cm²
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Answer: B) The 60° sector, by about 8.4 cm²
First sector = * 3.14 * 144 = 75.36 cm². Second = * 3.14 * 64 = 66.99 cm². So the 60° sector is larger by 75.36 - 66.99 = 8.37, about 8.4 cm². Doubling the angle does not make up for the radius dropping from 12 to 8, because the radius is SQUARED while the angle is not. The 251.2 cm² option compares the two whole circles (452.16 - 200.96) instead of the sectors.
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