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G8 Mensuration
Math quiz helps us to enhance brains neural network.
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1) A cylinder has a radius of 6 cm and height 10 cm, and a cone with the same radius is placed on top of the cylinder. If the slant height of the cone is 8 cm, find the total volume of the solid. (Use π = 3.14)
Volume of cylinder = πr²h = (3.14)(36)(10) = 1130.4 cm³ Volume of cone = (1/3)πr²h = (1/3)(3.14)(36)(8) = 301.44 cm³ Total volume = 1130.4 + 301.44 = 1431.84 cm³
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2) Find the height of a parallelogram with area 96 cm² and base 12 cm.
Area = base × height ⇒ 96 = 12 × h ⇒ h = 8 cm
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3) The volume of a sphere is 113.04 cm³. Find its radius. (Use π = 3.14)
V = (4/3)πr³ = 113.04 => r³ = (113.04 × 3) / (4 × 3.14) = 84.78 => r ≈ ∛84.78 ≈ 4.4 cm
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4) Find the area of a rhombus whose side is 10 cm and one diagonal is 12 cm.
Use Pythagoras to find other diagonal. Half of given diagonal = 6 Side² = (half_d1)² + (half_d2)² ⇒ 100 = 36 + x² ⇒ x² = 64 ⇒ x = 8 Second diagonal = 2×8 = 16 Area = (1/2) × d₁ × d₂ = (1/2)(12)(16) = 96 cm²
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5) The area of a trapezium is 180 cm² and its height is 12 cm. If one of the parallel sides is 15 cm, find the length of the other parallel side.
Use the formula for the area of a trapezium: A = (1/2) × (a + b) × h.
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6) If the edge of a cube is doubled, by what factor does its volume increase?
Original volume = a³ New volume = (2a)³ = 8a³ Factor = 8
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7) Find the volume of a hemisphere of radius 5 cm. (Use π = 3.14)
Volume of hemisphere = (2/3)πr³ ≈ (2/3)×3.14×125 ≈ 261.67 cm³.
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8) A cuboid measures 2.5 m × 2 m × 1.2 m. How many bricks of size 25 cm × 20 cm × 15 cm can be fitted into it?
Volume of cuboid = 2.5 × 2 × 1.2 = 6 m³ = 6000000 cm³ Volume of 1 brick = 25 × 20 × 15 = 7500 cm³ No. of bricks = 6000000 / 7500 = 800
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9) Find the curved surface area of a hemisphere of radius 10.5 cm. (Use π = 22/7)
CSA = 2πr² = 2(22/7)(10.5)² = 2(22/7)(110.25) = 693 cm²
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10) Find the total surface area of a cone of radius 7 cm and slant height 25 cm.
TSA = πr(l + r) = π(7)(25 + 7) = π(7)(32) = 224π ≈ 703.72 cm²
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11) A cylindrical tank has a diameter of 2.8 m and height 3 m. How many litres of water can it hold? (1 m³ = 1000 L)
Radius = 1.4 m Volume = πr²h = π(1.4)²(3) = π(1.96)(3) ≈ 18.47 m³ Capacity = 18.47 × 1000 = 18,470 L
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12) A rectangle of length 28 cm and width 14 cm has two semicircles of radius 7 cm attached to its shorter sides. What is the total area of the figure?
Area of rectangle = 28 × 14 = 392 cm² Area of 2 semicircles = 1 full circle = πr² = π(7²) = 49π ≈ 153.94 cm² Total area ≈ 392 + 153.94 = 545.94 cm²
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13) The radius of a circle is 14 cm. Find its area. (Use π = 22/7)
Area = πr² = (22/7)(14)² = 615.71 cm²
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14) A sector of a circle has a radius of 7 cm and a central angle of 60°. Find the area of the sector. (Use π = 22/7)
Area = (θ/360)πr² = (60/360)(22/7)(49) = 26.0 cm²
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15) A cylinder of radius 5 cm and height 10 cm is surmounted by a hemisphere. Find the total surface area of the solid.
CSA of cylinder = 2πrh = 2π(5)(10) = 100π CSA of hemisphere = 2πr² = 2π(25) = 50π Total SA = 150π = 471.24 cm²
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16) A conical vessel has radius 3.5 cm and height 10 cm. Find its volume. (Use π = 22/7)
V = (1/3)πr²h = (1/3)(22/7)(12.25)(10) = 128.3 cm³
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17) A cone is mounted on a cylinder. Radius of base is 3.5 cm, height of cylinder is 10 cm, and slant height of cone is 5 cm. Find the total surface area. (Use π = 22/7)
TSA = CSA of cone + CSA of cylinder + base area = πrl + 2πrh + πr² = (22/7)(3.5)(5) + 2(22/7)(3.5)(10) + (22/7)(3.5)² = 55 + 220 + 38.5 = 313.5 cm²
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18) A hemispherical bowl of radius 7 cm is filled with water. How much water can it hold?
Volume = (2/3)πr³ = (2/3)π(343) = 686π/3 ≈ 719.95 cm³
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19) Find the area of a sector of radius 21 cm and angle 60°. (Use π = 22/7)
Area = (θ/360) × πr² = (1/6)(22/7)(441) = (22×441)/(6×7) = 231 cm²
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20) The edge of a cube is 8 cm. Find its surface area.
TSA = 6a² = 6(8)² = 6(64) = 384 cm²
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