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Area Related Circles
10 MCQ Tests × 10 Questions = 100 Questions
Class 10 Mathematics practice tests based on the uploaded Area Related Circles question-and-answer PDF.
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TEST 1
Area Related Circles — MCQ Test 1
10 Questions
Q1. If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the new cylinder to the original cylinder is:
Correct Answer: Option C — 1 : 4
Q2. The circumference of a circle is 22 cm. The area of its quadrant is:
Correct Answer: Option C — 77/8 cm²
Q3. The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is:
Correct Answer: Option B — 2.1
Useful Resource: All Subjects Study Materials
Q4. If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle is:
Correct Answer: Option B — 26 cm
Q5. The end-points of a diameter of a circle are (2, 4) and (−3, −1). The radius of the circle is:
Correct Answer: Option C — 5/(2√2)
Q6. In Figure 1, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP is:
Correct Answer: Option A — 7.5 cm
Useful Resource: Ravi Test Papers
Q7. If the area of a sector of a circle bounded by an arc of length 5π cm is equal to 20π cm², then its radius is:
Correct Answer: Option C — 8 cm
Q8. If O is a fixed point and Q is a point which moves so that the distance OQ remains constant, the locus of Q is called:
Correct Answer: Option B — Circle
Q9. The area of the sector of angle 60° of a circle with radius 10 cm is:
Correct Answer: Option B — 550/21 cm²
Useful Resource: CBSE Class 10 English
Q10. The area of the incircle of an equilateral triangle of side 42 cm is:
Correct Answer: Option C — 462 cm²
TEST 2
Area Related Circles — MCQ Test 2
10 Questions
Q1. ABCD is a rectangle inscribed in a circle, with length 8 cm and breadth 6 cm. If π = 3.14, the area of the shaded region is:
Correct Answer: Option D — None of the above
Q2. The area of the largest triangle that can be inscribed in a semicircle of radius r is:
Correct Answer: Option A — r²
Q3. In the given figure, the area of segment ACB is:
Correct Answer: Option D — None of these
Useful Resource: Ravi Test Papers
Q4. ABCD is a square of side 4 cm. If E is an interior point such that △CED is equilateral, then the area of △ACE is:
Correct Answer: Option B — 4(√3 − 1) cm²
Q5. The area of the square that can be inscribed in a circle of radius 8 cm is:
Correct Answer: Option B — 128 cm²
Q6. The radius of a wheel is 0.25 m. How many revolutions will it make in covering 11 km?
Correct Answer: Option D — 7000
Useful Resource: CBSE Class 10 English
Q7. If π = 22/7, the distance (in metres) covered by a wheel of diameter 35 cm in one revolution is:
Correct Answer: Option B — 1.1
Q8. One side of a rhombus is 20 cm long and one of its diagonals measures 24 cm. The area of the rhombus is:
Correct Answer: Option D — 384 cm²
Q9. From the given figure, identify the centre of the circle.
Correct Answer: Option C — C
Useful Resource: Ravi Test Papers .in
Q10. To draw a pair of tangents to a circle inclined to each other at an angle of 45°, the angle between the corresponding radii is:
Correct Answer: Option B — 135°
TEST 3
Area Related Circles — MCQ Test 3
10 Questions
Q1. The radius of a circle is 20 cm. Three more concentric circles divide it into four parts of equal area. The radius of the largest of the three inner circles is:
Correct Answer: Option B — 10√3 cm
Q2. If the area of a sector bounded by an arc of length 5π cm is 20π cm², the radius of the circle is:
Correct Answer: Option C — 8 cm
Q3. A fixed point in a circle is called the _____ of the circle:
Correct Answer: Option B — Centre
Useful Resource: CBSE Class 10 English
Q4. Which piece is not required to complete the square, according to the given figure?
Correct Answer: Option C — J
Q5. The ratio of the areas of a circle and an equilateral triangle whose diameter and side respectively are equal is:
Correct Answer: Option B — π : √3
Q6. The angle described by the hour hand in 2 hours is:
Correct Answer: Option A — 60°
Useful Resource: Ravi Test Papers .in
Q7. The area of a sector of angle p° of a circle with radius R is:
Correct Answer: Option D — p/720 × 2πR²
Q8. The part of the circular region enclosed by two radii and the corresponding arc is called:
Correct Answer: Option C — A sector
Q9. A lighthouse throws light forming a sector of radius 21 m with central angle 120°. The area covered is:
Correct Answer: Option B — 462 m²
Useful Resource: CBSE Class 10 Maths
Q10. The area of the largest triangle that can be inscribed in a semicircle of radius r is:
Correct Answer: Option B — r²
TEST 4
Area Related Circles — MCQ Test 4
10 Questions
Q1. The area of the largest triangle that can be inscribed in a semicircle of radius r units is:
Correct Answer: Option A — r² sq. units
Q2. If a chord subtends an angle of 120° at the centre, the area of the corresponding segment is:
Correct Answer: Option B — (π/6 + √3/4)r²
Q3. Four circles each of radius a touch each other. The area between them is:
Correct Answer: Option C — (6/7)a²
Useful Resource: Ravi Test Papers .in
Q4. The area of a sector of a circle with radius 21 cm and sector angle 120° is:
Correct Answer: Option C — 462 cm²
Q5. If a chord subtends an angle of 60° at the centre, the area of the corresponding segment is:
Correct Answer: Option C — (π/6 − √3/4)r²
Q6. If a chord of a circle of radius 28 cm makes an angle of 90° at the centre, the area of the major segment is:
Correct Answer: Option D — 2240 cm²
Useful Resource: CBSE Class 10 Maths
Q7. In a circle of radius 14 cm, an arc subtends 120° at the centre. If √3 = 1.73, the area of the segment is:
Correct Answer: Option A — 120.56 cm²
Q8. In the given figure, the area of segment PAQ is:
Correct Answer: Option B — a²(π − 2)/4
Q9. If the area of a circle inscribed in an equilateral triangle is 48π square units, the perimeter of the triangle is:
Correct Answer: Option C — 72 units
Useful Resource: CBSE Class 10 Social Science
Q10. In the given figure, a square OABC is inscribed in the quadrant OPBQ. If OA = 20 cm and π = 3.14, the shaded area is:
Correct Answer: Option B — 228 cm²
TEST 5
Area Related Circles — MCQ Test 5
10 Questions
Q1. The radii of two concentric circles are 19 cm and 16 cm. The area of the ring enclosed by them is:
Correct Answer: Option B — 330 cm²
Q2. The angle described by the minute hand between 4:00 pm and 4:25 pm is:
Correct Answer: Option B — 150°
Q3. The area of a sector whose perimeter is four times its radius r is:
Correct Answer: Option C — r² sq. units
Useful Resource: CBSE Class 10 Maths
Q4. The area of a sector of a circle with radius r, making an angle of x° at the centre is:
Correct Answer: Option D — (x/360) × πr²
Q5. The area of a sector of angle p° of a circle with radius R is:
Correct Answer: Option A — p/720 × 2πR²
Q6. If a chord subtends a right angle at the centre, the area of the corresponding segment is:
Correct Answer: Option A — (π/4 − 1/2)r²
Useful Resource: CBSE Class 10 Social Science
Q7. If the sum of the areas of two circles with radii r₁ and r₂ equals the area of a circle of radius r, then:
Correct Answer: Option B — r₁² + r₂² = r²
Q8. A circle of radius 20 cm is divided into four equal-area parts by three concentric circles. The radius of the largest inner circle is:
Correct Answer: Option B — 10√3 cm
Q9. If the sum of the areas of two circles with radii R₁ and R₂ equals the area of a circle of radius R, then:
Correct Answer: Option B — R₁² + R₂² = R²
Useful Resource: RAVI MATHS TUITION CENTRE YouTube
Q10. If the area of a sector of a circle is 7/20 of the area of the circle, the sector angle is:
Correct Answer: Option D — 126°
TEST 6
Area Related Circles — MCQ Test 6
10 Questions
Q1. The area of a circle is 220 cm². The area of a square inscribed in it is:
Correct Answer: Option C — 140 cm²
Q2. Find the area of the shaded portion where the length is 14 units and the radius of the upper semicircle is 7 units:
Correct Answer: Option A — 196
Q3. A set of points equidistant from a fixed point in a plane is called a:
Correct Answer: Option B — Circle
Useful Resource: CBSE Class 10 Social Science
Q4. The length of the minute hand of a clock is 21 cm. The area swept by the minute hand in 10 minutes is:
Correct Answer: Option A — 231 cm²
Q5. The area of a sector of a circle with sector angle θ is given by:
Correct Answer: Option D — 2πr²θ/360
Q6. In the given figure, the ratio of the areas of two sectors S₁ and S₂ is:
Correct Answer: Option D — 4 : 5
Useful Resource: RAVI MATHS TUITION CENTRE YouTube
Q7. In the figure, if ABC is an equilateral triangle, the shaded area is equal to:
Correct Answer: Option A — (π/3 − √3/4)r²
Q8. The area of the sector of angle θ° of a circle with radius R is:
Correct Answer: Option D — πR²θ/360
Q9. In the given figure, the shaded area is:
Correct Answer: Option B — 25(π − 2) cm²
Useful Resource: CBSE Class 10 Science
Q10. If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, its area is:
Correct Answer: Option B — 52 cm²
TEST 7
Area Related Circles — MCQ Test 7
10 Questions
Q1. To draw a pair of tangents to a circle inclined to each other at angle x°, the angle between the corresponding radii is:
Correct Answer: Option B — 180° − x°
Q2. The length of an arc of a sector of angle θ° of a circle with radius R is:
Correct Answer: Option B — 2πRθ/360
Q3. If a chord of a circle of radius 14 cm subtends a right angle at the centre, the area of the sector is:
Correct Answer: Option B — 154 cm²
Useful Resource: RAVI MATHS TUITION CENTRE YouTube
Q4. If the area of a sector of a circle is 5/18 of the area of the circle, the sector angle is:
Correct Answer: Option C — 100°
Q5. If a line meets a circle in two distinct points, it is called a:
Correct Answer: Option B — Secant
Q6. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is:
Correct Answer: Option B — 22 cm
Useful Resource: CBSE Class 10 Science
Q7. The area of a sector of a circle whose radius is r units and whose arc length is l units is:
Correct Answer: Option D — (1/2)lr sq. units
Q8. A chord of a circle of radius 10 cm subtends a right angle at the centre. If π = 3.14, the area of the minor segment is:
Correct Answer: Option C — 28.5 cm²
Q9. The part of the circular region enclosed by a chord and the corresponding arc is called a:
Correct Answer: Option C — Segment
Useful Resource: All Subjects Study Materials
Q10. The perimeter of the sector OAB shown in the figure is:
Correct Answer: Option A — 64/3 cm
TEST 8
Area Related Circles — MCQ Test 8
10 Questions
Q1. What is the name of the shape shown in the figure?
Correct Answer: Option C — Circle
Q2. The radii of two concentric circles are 19 cm and 16 cm. The area of the ring enclosed between them is:
Correct Answer: Option D — 330 cm²
Q3. A shuttlecock used for playing badminton has the shape of a combination of:
Correct Answer: Option B — A frustum of a cone and a hemisphere
Useful Resource: CBSE Class 10 Science
Q4. The area of the largest triangle that can be inscribed in a semicircle of radius r units is:
Correct Answer: Option A — r² sq. units
Q5. In the given figure, the area of the shaded region is:
Correct Answer: Option A — 3π cm²
Q6. The area of the circle that can be inscribed in a square of side 6 cm is:
Correct Answer: Option D — 9π cm²
Useful Resource: All Subjects Study Materials
Q7. Assertion (A): A bicycle wheel makes 5000 revolutions in covering 11 km. Then the diameter of the wheel is 35 cm.
Reason (R): Area of a segment of a circle is θ/360 × πr² − (1/2)r²sinθ.
Choose the correct option:
Reason (R): Area of a segment of a circle is θ/360 × πr² − (1/2)r²sinθ.
Choose the correct option:
Correct Answer: Option D — Assertion (A) is false but reason (R) is true.
Q8. Assertion (A): In a circle of radius 6 cm, a sector has angle 60°. Then its area is 132/7 cm².
Reason (R): The area of a circle of radius r is πr².
Choose the correct option:
Reason (R): The area of a circle of radius r is πr².
Choose the correct option:
Correct Answer: Option B — Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
Q9. Assertion (A): Three points A, B, C are such that AB + BC > AC, then they are collinear.
Reason (R): Three points are collinear if they lie on a straight line.
Choose the correct option:
Reason (R): Three points are collinear if they lie on a straight line.
Choose the correct option:
Correct Answer: Option D — Assertion (A) is false but reason (R) is true.
Useful Resource: Ravi Test Papers
Q10. Assertion (A): The area of the sector of a circle of radius 5 cm is 9.75 cm² if the corresponding arc length is 3.5 cm.
Reason (R): The area of a sector of radius r and central angle θ is (θ/360°)πr².
Choose the correct option:
Reason (R): The area of a sector of radius r and central angle θ is (θ/360°)πr².
Choose the correct option:
Correct Answer: Option D — Assertion (A) is false but reason (R) is true.
TEST 9
Area Related Circles — MCQ Test 9
10 Questions
Q1. Assertion (A): A wire is looped in the form of a circle of radius 28 cm. It is bent into a square. Then the area of the square is 1936 cm².
Reason (R): The angle described by a minute hand in 60 minutes is 360°.
Choose the correct option:
Reason (R): The angle described by a minute hand in 60 minutes is 360°.
Choose the correct option:
Correct Answer: Option D — Assertion (A) is false but reason (R) is true.
Q2. Assertion (A): A bicycle wheel makes 5000 revolutions in covering 11 km. Then the diameter of the wheel is 35 cm.
Reason (R): The area of a segment of a circle is a sector area minus the corresponding triangle area.
Choose the correct option:
Reason (R): The area of a segment of a circle is a sector area minus the corresponding triangle area.
Choose the correct option:
Correct Answer: Option D — Assertion (A) is false but reason (R) is true.
Q3. Assertion (A): In a circle of radius 6 cm, a sector has angle 60°. Then its area is 186/7 cm².
Reason (R): The area of a circle with radius r is πr².
Choose the correct option:
Reason (R): The area of a circle with radius r is πr².
Choose the correct option:
Correct Answer: Option B — Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
Useful Resource: All Subjects Study Materials
Q4. Assertion (A): From a solid cylinder of height 12 cm and diameter 10 cm, a conical cavity of the same height and diameter is hollowed out. Then the volume of the cone is 2200/7 cm³.
Reason (R): If a conical cavity of the same height and diameter is hollowed from a cylinder, the cone's volume is half the cylinder's volume.
Choose the correct option:
Reason (R): If a conical cavity of the same height and diameter is hollowed from a cylinder, the cone's volume is half the cylinder's volume.
Choose the correct option:
Correct Answer: Option C — Assertion (A) is true but reason (R) is false.
Q5. Assertion (A): The sum of the length, breadth and height of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area is 236 cm².
Reason (R): The lateral surface area of a cuboid is 2(l + b).
Choose the correct option:
Reason (R): The lateral surface area of a cuboid is 2(l + b).
Choose the correct option:
Correct Answer: Option C — Assertion (A) is true but reason (R) is false.
Q6. Assertion (A): The volume of a hall, which is 5 times as high as it is broad and 8 times as long as it is high, is 12.8 m³. The breadth of the hall is 25 cm.
Reason (R): The total surface area of a cuboid of length l, breadth b and height h is 2(lb + bh + lh).
Choose the correct option:
Reason (R): The total surface area of a cuboid of length l, breadth b and height h is 2(lb + bh + lh).
Choose the correct option:
Correct Answer: Option D — Assertion (A) is false but reason (R) is true.
Useful Resource: Ravi Test Papers
Q7. Assertion (A): The number of spherical balls that can be made from a solid cube of lead of edge 44 cm, each ball being 4 cm in diameter, is 2541.
Reason (R): Number of balls = volume of lead ÷ volume of one ball.
Choose the correct option:
Reason (R): Number of balls = volume of lead ÷ volume of one ball.
Choose the correct option:
Correct Answer: Option C — Assertion (A) is true but reason (R) is false.
Q8. Assertion (A): If the areas of three adjacent faces of a cuboid are x, y, z respectively, then its volume is √xyz.
Reason (R): The volume of a cuboid whose edges are l, b and h is lbh cubic units.
Choose the correct option:
Reason (R): The volume of a cuboid whose edges are l, b and h is lbh cubic units.
Choose the correct option:
Correct Answer: Option A — Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Q9. Assertion (A): In the figure, O is the centre of a circle. If the area of sector OAPB is 5/18 of the area of the circle, then x = 100°.
Reason (R): The length of an arc of radius r and central angle θ is (θ/360°)πr².
Choose the correct option:
Reason (R): The length of an arc of radius r and central angle θ is (θ/360°)πr².
Choose the correct option:
Correct Answer: Option C — Assertion (A) is true but reason (R) is false.
Useful Resource: CBSE Class 10 English
Q10. Assertion (A): The length of the minute hand of a clock is 7 cm. The area swept by the minute hand in 5 minutes is 125/6 cm².
Reason (R): The length of an arc of a sector of angle θ and radius r is (θ/360°) × 2πr.
Choose the correct option:
Reason (R): The length of an arc of a sector of angle θ and radius r is (θ/360°) × 2πr.
Choose the correct option:
Correct Answer: Option B — Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
TEST 10
Area Related Circles — MCQ Test 10
10 Questions
Q1. Assertion (A): The area of the square inscribed in a circle of radius r is 2r² sq. units.
Reason (R): Area of the major segment of a circle = area of the circle − area of the minor segment.
Choose the correct option:
Reason (R): Area of the major segment of a circle = area of the circle − area of the minor segment.
Choose the correct option:
Correct Answer: Option D — Assertion (A) is false but reason (R) is true.
Q2. Pihu's umbrella has 10 equally spaced ribs and is assumed to be a flat circle. The central angle between two consecutive ribs is:
Correct Answer: Option A — 36°
Q3. For Pihu's umbrella of radius 50 cm with 10 equally spaced ribs, the area between two consecutive ribs is:
Correct Answer: Option B — 785.71 cm²
Useful Resource: Ravi Test Papers
Q4. For Pihu's umbrella, the formula used to calculate the area between two consecutive ribs is:
Correct Answer: Option C — (θ/360°)πr²
Q5. If Pihu's umbrella had only 8 ribs, the central angle between two consecutive ribs would be:
Correct Answer: Option A — 45°
Q6. If Pihu's umbrella had only 8 ribs and radius 50 cm, the area between two consecutive ribs would be:
Correct Answer: Option B — 982.14 cm²
Useful Resource: CBSE Class 10 English
Q7. Gayatri has a triangular field with sides 25 m, 24 m and 7 m. The area of the triangular field is:
Correct Answer: Option B — 84 m²
Q8. In Gayatri's field, a cow is tied at a corner with a rope of 3.5 m. The area grazed by the cow is:
Correct Answer: Option A — (∠A/360°) × π × (3.5)²
Q9. In Gayatri's field, the area grazed by the buffalo and horse together is:
Correct Answer: Option D — ((∠B+∠C)/360°) × π × (3.5)²
Useful Resource: Ravi Test Papers .in
Q10. Priya wants to divide a circular cake equally among 12 people. How many diameters need to be considered to divide the cake into 12 equal pieces?
Correct Answer: Option B — 6
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