Let’s solve each problem one by one. We’ll use the right volume formulas for each shape and plug in the numbers carefully.
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Problem 1: Cylindrical water bottle
Radius = 5 cm, Height = 20 cm
Volume of cylinder = π × r² × h
= 3.14 × (5)² × 20
= 3.14 × 25 × 20
= 3.14 × 500
=
1570 cubic centimeters
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Problem 2: Rectangular dumbbell
Dimensions: 15 in × 5 in × 3 in
Volume of rectangular prism = length × width × height
= 15 × 5 × 3
= 75 × 3
=
225 cubic inches
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Problem 3: Gym locker (rectangular prism)
Dimensions: 12 in × 15 in × 18 in
Volume = 12 × 15 × 18
First: 12 × 15 = 180
Then: 180 × 18 = let’s break it down → 180 × 10 = 1800, 180 × 8 = 1440 → total = 1800 + 1440 =
3240 cubic inches
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Problem 4: Soccer ball (sphere)
Radius = 11 cm
Volume of sphere = (4/3) × π × r³
= (4/3) × 3.14 × (11)³
First, 11³ = 11 × 11 × 11 = 121 × 11 = 1331
Now: (4/3) × 3.14 × 1331
First, 3.14 × 1331 ≈ let’s calculate:
3 × 1331 = 3993
0.14 × 1331 ≈ 186.34
Total ≈ 3993 + 186.34 = 4179.34
Now multiply by 4/3:
(4/3) × 4179.34 ≈ (4 × 4179.34) ÷ 3
4 × 4179.34 = 16717.36
Divide by 3: 16717.36 ÷ 3 ≈
5572.45 cubic centimeters
*(Note: Some teachers use π = 3.14, others use more precise values — we’ll stick with 3.14 as implied by other problems.)*
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Problem 5: Cylindrical buoy
Radius = 3 feet, Height = 4 feet
Volume = π × r² × h
= 3.14 × (3)² × 4
= 3.14 × 9 × 4
= 3.14 × 36
=
113.04 cubic feet
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Problem 6: Conical water bottle
Radius = 6 cm, Height = 12 cm
Volume of cone = (1/3) × π × r² × h
= (1/3) × 3.14 × (6)² × 12
= (1/3) × 3.14 × 36 × 12
First, 36 × 12 = 432
Then, 3.14 × 432 = let’s compute:
3 × 432 = 1296
0.14 × 432 = 60.48
Total = 1296 + 60.48 = 1356.48
Now divide by 3: 1356.48 ÷ 3 =
452.16 cubic centimeters
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Problem 7: Weightlifting plate (cylinder)
Radius = 8 inches, Thickness (height) = 2 inches
Volume = π × r² × h
= 3.14 × (8)² × 2
= 3.14 × 64 × 2
= 3.14 × 128
=
401.92 cubic inches
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Problem 8: Yoga mat rolled into cylinder
Radius = 4 inches, Length (height) = 72 inches
Volume = π × r² × h
= 3.14 × (4)² × 72
= 3.14 × 16 × 72
First, 16 × 72 = 1152
Then, 3.14 × 1152
Break it down:
3 × 1152 = 3456
0.14 × 1152 = 161.28
Total = 3456 + 161.28 =
3617.28 cubic inches
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Problem 9: Weightlifting barbell (cylinder)
Radius = 1 inch, Length = 72 inches
Volume = π × r² × h
= 3.14 × (1)² × 72
= 3.14 × 1 × 72
=
226.08 cubic inches
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Problem 10: Swimming pool (rectangular prism)
Dimensions: 20 m × 10 m × 2 m
Volume = length × width × depth
= 20 × 10 × 2
= 200 × 2
=
400 cubic meters
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Final Answer:
1. 1570 cm³
2. 225 in³
3. 3240 in³
4. 5572.45 cm³
5. 113.04 ft³
6. 452.16 cm³
7. 401.92 in³
8. 3617.28 in³
9. 226.08 in³
10. 400 m³
Parent Tip: Review the logic above to help your child master the concept of volume of a cylinder word problems worksheet pdf.
