Free Area and Volume MCQs with Answers
204 Area and Volume MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.
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204 questions · page 3 of 11
41. If the side of a square is increased by 25 % then how much percent does it's area get increased:
- A. 125
- B. 156.25
- C. 50
- D. 56.25
Explanation: Increasing the side by 25% makes it 1.25 times the original, so the area becomes 1.25² = 1.5625 times the original.
Correct answer: 56.25- A. 260m
- B. 280m
- C. 360m
- D. None of these
Explanation: Let the length and breadth be 5x m and 4x m. Their difference is x m, so x = 20 m; hence the dimensions are 100 m and 80 m, and the…
Correct answer: 360m- A. 50m
- B. 100m
- C. 150m
- D. 200m
Explanation: The total surrounding cost gives the perimeter: 3000 rupees ÷ 7.50 rupees per metre = 400 m.
Correct answer: 50m- A. 37
- B. 38
- C. 39
- D. 40
Explanation: The playground perimeter is 2(36 m + 21 m) = 114 m. At a spacing of 3 m, the number of equal boundary intervals, and therefore flag staffs…
Correct answer: 38- A. 20
- B. 30
- C. 60
- D. None of these
Explanation: The playground is one-third of the plot, so the plot area is 3 × 1200 m² = 3600 m².
Correct answer: None of these46. If the length of diagonal AC of a square ABCD is 5.2 cm then area of the square ABCD is_________?
- A. 15.12 sq.cm
- B. 13.52 sq.cm
- C. 12.62 sq.cm
- D. 10 sq.cm
Explanation: For a square, the diagonal satisfies d² = 2A, so A = d² ÷ 2 = (5.2 cm)² ÷ 2 = 27.04 cm² ÷ 2 = 13.52 cm².
Correct answer: 13.52 sq.cm- A. 160m × 27m
- B. 240m × 18m
- C. 120m × 36m
- D. 135m × 32m
Explanation: Let the smaller side be b m. Three squares first use 3b m of the longer side, and the remaining strip is divided into three squares, so…
Correct answer: 120m × 36m- A. A square with an area of 36 sq.cm
- B. An Equilateral Triangle with a side of 9 cm
- C. A rectangle with 10 cm as length and 40 sq.cm as area
- D. A circle with a radius of 4 cm
Explanation: The square has side √36 cm² = 6 cm, so its perimeter is 24 cm. The triangle perimeter is 3 × 9 cm = 27 cm, the rectangle has breadth 40…
Correct answer: A rectangle with 10 cm as length and 40 sq.cm as area49. The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
- A. 26.4 m2
- B. 39.6 m2
- C. 52.8 m2
- D. 79.2 m2
Explanation: A sector's area is (angle ÷ 360°) × πr². Substituting gives (42° ÷ 360°) × π × (12 m)² = 16.8π m² = 52.8 m² using π = 22/7.
Correct answer: 52.8 m2- A. 0.35 cm2
- B. 17.5 cm2
- C. 8.75 cm2
- D. 55 cm2
Explanation: For a sector, area = 1/2 × radius × arc length. Therefore the area is 1/2 × 5 cm × 3.5 cm = 8.75 cm².
Correct answer: 8.75 cm2- A. (400 - 100π) cm2</sup
- B. (400 - 2π) cm2</sup
- C. (400 - 200π) cm2</sup
- D. 200π cm2</sup
Explanation: Each semicircle has diameter 20 cm, so radius 10 cm; the two semicircles together form one circle of area π(10 cm)² = 100π cm².
Correct answer: (400 - 100π) cm2</sup- A. Rs.45
- B. Rs.78
- C. Rs.44
- D. Rs.40
Explanation: The walk is an annulus with outer radius 15 m and inner radius 13 m, so its area is π[(15 m)² - (13 m)²] = 56π m² = 176 m².
Correct answer: Rs.44- A. 25 cm
- B. 28 cm
- C. 30 cm
- D. 35 cm
Explanation: The perimeter of a semicircle includes its curved part and diameter, so P = πr + 2r.
Correct answer: 28 cm- A. 35.4 cm
- B. 32.4 cm
- C. 32 cm
- D. 30 cm
Explanation: A semicircle's perimeter is πr + 2r, including the diameter. With r = 6.3 cm, P = (22/7 × 6.3 cm) + 12.6 cm = 19.8 cm + 12.6 cm = 32.4 cm.
Correct answer: 32.4 cm- A. 1120 m2
- B. 1250 m2
- C. 1210 m2
- D. 1200 m2
Explanation: The extra grazing area is the annulus formed when the radius increases from 12 m to 23 m: π[(23 m)² - (12 m)²] = 385π m² = 1210 m² using π…
Correct answer: 1210 m256. Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
- A. Rs.150
- B. Rs.132
- C. Rs.100
- D. Rs.125
Explanation: The field's circumference is πd = (22/7) x 28 m = 88 m. Fencing cost = 88 m x Rs.1.50 per m = Rs.132, so option b follows.
Correct answer: Rs.132- A. 124 sq m
- B. 154 sq m
- C. 145 sq m
- D. 167 sq m
Explanation: The area of a circle is πr², so A = (22/7) x 7 m x 7 m = 154 m². Therefore option b is correct.
Correct answer: 154 sq m- A. 20 m
- B. 60 m
- C. 40 m
- D. 80 m
Explanation: The trapezium area is 1/2 x (sum of parallel sides) x depth. Therefore 640 m² = 1/2 x (10 m + 6 m) x depth = 8 m x depth, so depth = 640…
Correct answer: 80 m- A. 8 m
- B. 10 m
- C. 6 m
- D. 12 m
Explanation: Let the base be b m. The altitude is twice the base, so it is 2b m, and the parallelogram area is b x 2b = 2b² = 128 m².
Correct answer: 8 m- A. 260 cm2
- B. 240 cm2
- C. 280 cm2
- D. 220 cm2
Explanation: A rhombus has four equal sides, so each side is 68 cm / 4 = 17 cm. Half of the 16 cm diagonal is 8 cm, and the other half is √(17² - 8²)…
Correct answer: 240 cm2