Let’s solve each problem one by one. We’ll use the correct volume formulas and round to the nearest tenth as instructed.
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1) Cone: radius = 4 ft, height = 12 ft
Volume of cone = (1/3)πr²h
= (1/3) × π × 4² × 12
= (1/3) × π × 16 × 12
= (1/3) × 192π
= 64π ≈ 64 × 3.1416 ≈
201.1 ft³
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2) Sphere: diameter = 12 cm → radius = 6 cm
Volume of sphere = (4/3)πr³
= (4/3) × π × 6³
= (4/3) × π × 216
= 288π ≈ 288 × 3.1416 ≈
904.8 cm³
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3) Sphere: radius = 5.9 km
Volume = (4/3)πr³
= (4/3) × π × (5.9)³
First, 5.9³ = 5.9 × 5.9 × 5.9 = 34.81 × 5.9 = 205.379
Then, (4/3) × 205.379 × π ≈ (273.8387) × π ≈ 273.8387 × 3.1416 ≈
860.3 km³
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4) Sphere: radius = 4.7 mi
Volume = (4/3)πr³
= (4/3) × π × (4.7)³
4.7³ = 4.7 × 4.7 × 4.7 = 22.09 × 4.7 = 103.823
(4/3) × 103.823 ≈ 138.4307
× π ≈ 138.4307 × 3.1416 ≈
434.9 mi³
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5) Sphere: radius = 2 in
Volume = (4/3)πr³
= (4/3) × π × 8
= (32/3)π ≈ 10.6667 × 3.1416 ≈
33.5 in³
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6) Cone: radius = 4 in, height = 8 in
Volume = (1/3)πr²h
= (1/3) × π × 16 × 8
= (1/3) × 128π ≈ 42.6667 × 3.1416 ≈
134.0 in³
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7) Cylinder: radius = 5 mi, height = 11 mi
Volume = πr²h
= π × 25 × 11
= 275π ≈ 275 × 3.1416 ≈
863.9 mi³
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8) Cylinder: diameter = 18 m → radius = 9 m, height = 10 m
Volume = πr²h
= π × 81 × 10
= 810π ≈ 810 × 3.1416 ≈
2544.7 m³
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9) Cone: radius = 1 ft, height = 11 ft
Volume = (1/3)πr²h
= (1/3) × π × 1 × 11
= (11/3)π ≈ 3.6667 × 3.1416 ≈
11.5 ft³
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10) Cylinder: radius = 4 km, height = 8 km
Volume = πr²h
= π × 16 × 8
= 128π ≈ 128 × 3.1416 ≈
402.1 km³
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Final Answer:
1) 201.1 ft³
2) 904.8 cm³
3) 860.3 km³
4) 434.9 mi³
5) 33.5 in³
6) 134.0 in³
7) 863.9 mi³
8) 2544.7 m³
9) 11.5 ft³
10) 402.1 km³
Parent Tip: Review the logic above to help your child master the concept of volume of cylinder cones and spheres worksheet.
