All Free Mathematics MCQs with Answers

• 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.

• 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.

• 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.

• 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…

• 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.

• 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…

• 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…

• A. 30 π cc
• B. 45 π cc
• C. 150 π cc
• D. 180 π cc

Explanation: The diameter is 6 cm, so the radius is 3 cm. The cylinder's volume is πr²h = π × (3 cm)² × 5 cm = 45π cm³.

• A. 18 πr2 sq units
• B. 3 πr2 sq units
• C. 12 πr2 sq units
• D. 6 πr2 sq units

Explanation: The curved surface area of a cylinder is 2πrh. With r = 2r units and h = 3r units, it becomes 2π × 2r × 3r = 12πr² square units.

• A. 2.66 cm
• B. 2.5 cm
• C. 3 cm
• D. 3.5 cm

Explanation: For spheres, volume is proportional to the cube of the diameter, so 3³ cm³ = (1.5 cm)³ + (2 cm)³ + d³.

• A. 100π
• B. 7π
• C. 60π
• D. 50π

Explanation: Eight equal balls have one-eighth of the original sphere's volume, so each ball has radius 10 cm ÷ 2 = 5 cm because volume scales with the…

• A. 1:4
• B. 1:16
• C. 1:8
• D. 1:64

Explanation: Sphere area is proportional to r², so an area ratio of 1:4 gives a radius ratio of 1:2.

• A. 6:25
• B. 3:5
• C. 9:25
• D. 16:25

Explanation: Cube volume is proportional to the cube of its edge, so a volume ratio of 27:125 gives an edge ratio of 3:5.

• A. 15840 m
• B. 16840 m
• C. 15820 m
• D. 15640 m

Explanation: The square's side is √69696 m² = 264 m. Its perimeter is 4 × 264 m = 1056 m, and 15 rounds require 15 × 1056 m = 15840 m of wire.

• A. 8 cm
• B. 12 cm
• C. 14 cm
• D. 10 cm

Explanation: The total volume of the melted cubes is 6³ cm³ + 8³ cm³ + 10³ cm³ = 216 cm³ + 512 cm³ + 1000 cm³ = 1728 cm³.

• A. 3:1
• B. 8:1
• C. 9:1
• D. 12:1

Explanation: The total surface area of a cube is 6a², so surface area varies as the square of its side.

• A. 5 cm
• B. 19 cm
• C. 13 cm
• D. 144 cm

Explanation: The diagonal of a cuboid is √(l² + b² + h²). Thus it is √[(3 cm)² + (4 cm)² + (12 cm)²] = √(9 cm² + 16 cm² + 144 cm²) = √169 cm² = 13 cm.

• A. 120 cm2
• B. 148 cm2
• C. 74 cm2
• D. 15 cm2

Explanation: The surface area of a cuboid is 2(lw + lh + wh), so 2[(4 cm x 5 cm) + (4 cm x 6 cm) + (5 cm x 6 cm)] = 2(20 + 24 + 30) cm2 = 148 cm2.

• A. 3 dm
• B. 4 dm
• C. 5 dm
• D. 6 dm

Explanation: The combined volume is 3^3 dm3 + 4^3 dm3 + 5^3 dm3 = 27 dm3 + 64 dm3 + 125 dm3 = 216 dm3.

• A. 50
• B. 64
• C. 216
• D. 125

Explanation: A metre cube has side 10 dm. Along each dimension, 10 dm ÷ 2 dm = 5 cubes fit, so the total number is 5 x 5 x 5 = 125 cubes.