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 8 of 11
- A. 1390 cm2
- B. 695 cm2
- C. 1280 cm2
- D. 1220 cm2
Explanation: For a closed rectangular box, cardboard area is 2(lb + bh + lh). Substituting 25 cm, 15 cm and 8 cm gives 2[(25 cm x 15 cm) + (15 cm x 8…
Correct answer: 1390 cm2- A. 4500 M3
- B. 27000 M3
- C. 3000 M3
- D. 2700 M3
Explanation: The river's cross-sectional area is 2 m x 45 m = 90 m2. Its speed is 3 km/h = 3000 m/h = 50 m/min, so the water flowing each minute is 90…
Correct answer: 4500 M3- A. 8.56 kg
- B. 7.76 kg
- C. 7.756 kg
- D. 6.832 kg
Explanation: Taking 52 cm x 40 cm x 29 cm as the outside dimensions of an open box, the inside dimensions are 48 cm x 36 cm x 27 cm because the 2 cm…
Correct answer: 6.832 kg144. The ratio of the volumes of a cube to that of the sphere which will fit inside the cube is________?
- A. 4:3
- B. 4:2
- C. 4:4
- D. 6: π
Explanation: If a sphere fits inside a cube, its diameter equals the cube's side, say a.
Correct answer: 6: π- A. Rs.60
- B. Rs.57
- C. Rs.55
- D. Rs.52
Explanation: The area of the four walls is 2h(l + b) = 2 x 3 m x (15 m + 4 m) = 114 m2.
Correct answer: Rs.57- A. 1000
- B. 600
- C. 2400
- D. 1200
Explanation: The floor area is 30 m x 20 m = 600 m2. A carpet strip 50 cm wide has width 0.5 m, so its required length is 600 m2 / 0.5 m = 1200 m.
Correct answer: 1200- A. 25 m
- B. 35 m
- C. 45 m
- D. 50 m
Explanation: At 50 paise per m2, or Rs.0.50 per m2, an expenditure of Rs.600 covers 600 / 0.50 = 1200 m2.
Correct answer: 50 m- A. 4:3
- B. 16:9
- C. 64:27
- D. 3:4
Explanation: The space diagonal of a cube with side s is s√3, so the common factor √3 does not change the ratio.
Correct answer: 4:3- A. 21 cm
- B. 19 cm
- C. 32 cm
- D. 18 cm
Explanation: Because the metal is melted without loss, the new cube's volume is the sum of the original volumes: 9 cm cubed + 12 cm cubed + 15 cm cubed…
Correct answer: 18 cm- A. 27:1
- B. 1:27
- C. 1:9
- D. 9:1
Explanation: Sphere volume is proportional to the cube of its radius, V = 4/3 pi r3. Thus radii 1:3 give volumes 1 cubed:3 cubed = 1:27.
Correct answer: 1:27- A. 36
- B. 64
- C. 27
- D. 16
Explanation: The number of smaller spherical shots is the ratio of volumes, not the ratio of radii.
Correct answer: 27- A. 3:4
- B. 4:3
- C. 3:1
- D. 1:3Everyday Science Quiz
Explanation: The whole surface area of a sphere is 4pi r2, while the total surface area of a hemisphere, including its circular base, is 3pi r2.
Correct answer: 4:3- A. 1 cm
- B. 2 cm
- C. 4 cm
- D. 3 cm
Explanation: The curved surface area of a sphere is 4πr². Thus 4πr² = 64π, so r² = 16 cm² and r = 4 cm.
Correct answer: 4 cm- A. 74 π cm2
- B. 36 π cm2
- C. 48 π cm2
- D. 24 π cm2
Explanation: The curved surface area of a cone is πrl, where r = 4 cm and l = 12 cm. Therefore, π × 4 cm × 12 cm = 48π cm².
Correct answer: 48 π cm2- A. 120 cm3
- B. 40 cm3
- C. 50 cm3
- D. 60 cm3
Explanation: The volume of a cone is one-third of its base area multiplied by its height. So V = 1/3 × 30 cm² × 6 cm = 60 cm³.
Correct answer: 60 cm3- A. 12 π cm3
- B. 6 π cm3
- C. 8 π cm3
- D. 10 π cm3
Explanation: Using V = 1/3πr²h, the volume is 1/3 × π × (3 cm)² × 4 cm = 1/3 × π × 9 cm² × 4 cm = 12π cm³.
Correct answer: 12 π cm3- A. 1:2
- B. 2:1
- C. 1:4
- D. 4:1
Explanation: The curved surface area of a cylinder is 2πrh. Since the heights are equal, 2πh is common to both cylinders, so their curved surface areas…
Correct answer: 1:2- A. 360 cc
- B. 60 cc
- C. 300 cc
- D. 36 cc
Explanation: Cylinder volume is πr²h, so with equal heights the volume ratio is the square of the radius ratio: 1²:3² = 1:9.
Correct answer: 360 cc- A. Rs.1185
- B. Rs.1285
- C. Rs.1385
- D. Rs.1485
Explanation: The well is a cylinder with radius 3 m ÷ 2 = 1.5 m and height 14 m. Its volume is π × (1.5 m)² × 14 m = 31.5π m³ = 99 m³ using π = 22/7…
Correct answer: Rs.1485160. The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
- A. 308 sq cm
- B. 220 sq cm
- C. 440 sq cm
- D. 132 sq cm
Explanation: The whole surface area of a closed cylinder is 2πr(h + r). Substituting r = 7 cm and h = 3 cm gives 2π × 7 cm × 10 cm = 140π cm² = 440 cm²…
Correct answer: 440 sq cm