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 10 of 11
- A. 2 : 1
- B. 3 : 2
- C. 25 : 18
- D. 27 : 20
Explanation: The total surface area of the three small cubes is 6(3 cm)^2 + 6(4 cm)^2 + 6(5 cm)^2 = 54 cm2 + 96 cm2 + 150 cm2 = 300 cm2.
Correct answer: 25 : 18- A. 4920 cm2
- B. 4727 cm2
- C. 9856 cm2
- D. 19712 cm2
Explanation: Sphere surface area is proportional to r^2. Doubling the radius makes the surface area four times as large, so the new area is 4 x 2464…
Correct answer: 9856 cm2- A. 4 : 3
- B. 8 : 7
- C. 4 : 1
- D. 6 : 5
Explanation: Let the original dimensions be 3k and 2k, so the perimeter is 10k. If the new dimensions are 7m and 3m, their perimeter is 20m, giving m =…
Correct answer: 8 : 7- A. 91.5 cm
- B. 93.5 cm
- C. 94.5 cm
- D. 92.5 cm
Explanation: The arc length is (135°/360°) x 2π x 21 cm = 15.75π cm = 49.5 cm, using π = 22/7.
Correct answer: 91.5 cm- A. 140
- B. 156
- C. 175
- D. 214
Explanation: The square's side is √1225 sq.units = 35 units, so the circle's radius is 35 units.
Correct answer: 140186. The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
- A. 81 : 121
- B. 9 : 11
- C. 729 : 1331
- D. 27 : 12Everyday Science Quiz
Explanation: For cubes, volume is proportional to the cube of the side, so the side ratio is ∛(729 : 1331) = 9 : 11.
Correct answer: 81 : 121- A. 45 cm
- B. 18 cm
- C. 90 cm
- D. None of these
Explanation: Equating the volumes, (4/3)π(12 cm)^3 = π(16 cm)^2L. Thus L = [4 x 12^3 cm^3]/[3 x 16^2 cm^2] = 9 cm.
Correct answer: None of these- A. 252 m
- B. 704 m
- C. 352 m
- D. 808 m
Explanation: One revolution covers the wheel's circumference: 2π x 22.4 cm = 140.8 cm, using π = 22/7.
Correct answer: 704 m- A. Rs. 4800
- B. Rs. 3600
- C. Rs. 3560
- D. Rs. 4530
Explanation: The area of the four walls is 2(25 ft + 15 ft) x 12 ft = 960 sq.ft. Openings occupy 6 ft x 3 ft = 18 sq.ft and 3 x (4 ft x 3 ft) = 36…
Correct answer: Rs. 4530- A. 10
- B. 100
- C. 1000
- D. 10000
Explanation: Each 1 m edge is 100 cm, so each edge contains 100 cm ÷ 10 cm = 10 small cubes. The total number is 10 x 10 x 10 = 1,000 cubes.
Correct answer: 1000- A. 12 π cm
- B. 16 π cm
- C. 24 π cm
- D. 32 π cm
Explanation: The square has side √196 sq.cm = 14 cm, and this is half the larger circle's radius, so the larger radius is 28 cm.
Correct answer: 24 π cm- A. 3.34
- B. 2
- C. 4.5
- D. 5.5
Explanation: The garden radius is 4 m ÷ 2 = 2 m, and the path increases it to 2.25 m because 25 cm = 0.25 m.
Correct answer: 3.34- A. 4192 sq m
- B. 4304 sq m
- C. 4312 sq m
- D. 4360 sq m
Explanation: Using C = 2πr, the radii are 264 m ÷ (2 x 22/7) = 42 m and 352 m ÷ (2 x 22/7) = 56 m.
Correct answer: 4312 sq m- A. 200 sq cm
- B. 72 sq cm
- C. 162 sq cm
- D. Cannot be determined
Explanation: The rectangle's area is length x breadth = 480 sq.cm, but this does not determine its perimeter because many length and breadth pairs have…
Correct answer: Cannot be determined- A. 18 : 5
- B. 7 : 16
- C. 5 : 14
- D. None of these
Explanation: The square's side is √4096 sq.cm = 64 cm. The rectangle's length is 2 x 64 cm = 128 cm and its breadth is 64 cm - 24 cm = 40 cm, so…
Correct answer: None of these- A. Rs. 3642.40
- B. Rs. 3868.80
- C. Rs. 4216.20
- D. Rs. 4082.40
Explanation: The original length is 1.44 x 6 m = 8.64 m. The new dimensions are 8.64 x 1.40 = 12.096 m and 6 x 1.25 = 7.5 m, so the area is 12.096 x…
Correct answer: Rs. 4082.40- A. 27 m
- B. 24 m
- C. 18 m
- D. 21 m
Explanation: An increase of 200% means the length is 300% of the breadth, so length = 3 x breadth. The painted area is Rs. 324 ÷ Rs.
Correct answer: 18 m- A. 8.5 m
- B. 17 m
- C. 34 m
- D. 51 m
Explanation: Let the breadth be b m, so the length is 3b m. Then 3b2 = 867 m2, giving b2 = 289 m2 and b = 17 m.
Correct answer: 17 m- A. 8
- B. 12
- C. 6
- D. 2
Explanation: If the sides are a and b units, the square on the diagonal has area a2 + b2, while the rectangle has area ab.
Correct answer: 2- A. 1 : 96
- B. 1 : 48
- C. 1 : 84
- D. 1 : 68
Explanation: Write the sides as 4x cm and 3x cm. Since 12x2 cm2 = 6912 cm2, x2 = 576 cm2 and x = 24 cm, so the breadth is 72 cm; therefore breadth:area…
Correct answer: 1 : 96