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Volume worksheet

Grades 6–8 · CCSS 6.G.A.2, 8.G.C.9

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Shape: Sphere
- Measurement unit: Millimeters (mm)
- Radius: 2
Find: Volume
Answer
2.
Problem 2.
- Shape: Sphere
- Measurement unit: Feet (ft)
- Radius: 1.8
Find: Volume
Answer
3.
Problem 3.
- Shape: Rectangular box (cuboid)
- Measurement unit: Meters (m)
- Length: 3
- Width: 3
- Height: 2
Find: Volume
Answer
4.
Problem 4.
- Shape: Cube
- Measurement unit: Centimeters (cm)
- Edge length: 3
Find: Volume
Answer
5.
Problem 5.
- Shape: Cone
- Measurement unit: Meters (m)
- Radius: 1.8
- Height: 2
Find: Volume
Answer
6.
Problem 6.
- Shape: Rectangular box (cuboid)
- Measurement unit: Feet (ft)
- Length: 3
- Width: 3
- Height: 2
Find: Volume
Answer
7.
Problem 7.
- Shape: Rectangular pyramid
- Measurement unit: Yards (yd)
- Length: 6
- Width: 3
- Height: 3
Find: Volume
Answer
8.
Problem 8.
- Shape: Rectangular box (cuboid)
- Measurement unit: Feet (ft)
- Length: 5
- Width: 2
- Height: 2
Find: Volume
Answer
9.
Problem 9.
- Shape: Cone
- Measurement unit: Yards (yd)
- Radius: 1.1
- Height: 2
Find: Volume
Answer
10.
Problem 10.
- Shape: Cube
- Measurement unit: Millimeters (mm)
- Edge length: 1
Find: Volume
Answer

Answer key: Volume worksheet

1. Volume: 33.51 mm³
1. For a sphere, multiply 4/3 by π and by the radius three times
  $\frac{4}{3} \times π \times 2^{3}$ $= 33.510322 mm³$
2. Convert to liters: 1 mm³ = 0.000001 L
  $33.510322 mm³ \times 0.000001$ $= 0.000034 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{0.000034 L}{3.785411784}$ $= 0.000009 US gal$
2. Volume: 24.43 ft³
1. For a sphere, multiply 4/3 by π and by the radius three times
  $\frac{4}{3} \times π \times {1.8}^{3}$ $= 24.429024 ft³$
2. Convert to liters: 1 ft³ = 28.31684659 L
  $24.429024 ft³ \times 28.31684659$ $= 691.752938 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{691.752938 L}{3.785411784}$ $= 182.741793 US gal$
3. Volume: 18 m³
1. Multiply the length, width and height of the box
  $3 \times 3 \times 2$ $= 18 m³$
2. Convert to liters: 1 m³ = 1,000 L
  $18 m³ \times 1,000$ $= 18,000 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{18,000 L}{3.785411784}$ $= 4,755.096942 US gal$
4. Volume: 27 cm³
1. A cube's length, width and height are all the same edge, so multiply the edge by itself three times
  $3^{3}$ $= 27 cm³$
2. Convert to liters: 1 cm³ = 0.001 L
  $27 cm³ \times 0.001$ $= 0.027 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{0.027 L}{3.785411784}$ $= 0.007133 US gal$
5. Volume: 6.79 m³
1. A cone holds one third of a cylinder with the same base and height, so take 1/3 × π × radius² × height
  $\frac{1}{3} \times π \times {1.8}^{2} \times 2$ $= 6.78584 m³$
2. Convert to liters: 1 m³ = 1,000 L
  $6.78584 m³ \times 1,000$ $= 6,785.840132 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{6,785.840132 L}{3.785411784}$ $= 1,792.629315 US gal$
6. Volume: 18 ft³
1. Multiply the length, width and height of the box
  $3 \times 3 \times 2$ $= 18 ft³$
2. Convert to liters: 1 ft³ = 28.31684659 L
  $18 ft³ \times 28.31684659$ $= 509.703239 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{509.703239 L}{3.785411784}$ $= 134.649351 US gal$
7. Volume: 18 yd³
1. A pyramid holds one third of a box with the same base and height, so take 1/3 × length × width × height
  $\frac{1}{3} \times 6 \times 3 \times 3$ $= 18 yd³$
2. Convert to liters: 1 yd³ = 764.55485798 L
  $18 yd³ \times 764.55485798$ $= 13,761.987444 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{13,761.987444 L}{3.785411784}$ $= 3,635.532468 US gal$
8. Volume: 20 ft³
1. Multiply the length, width and height of the box
  $5 \times 2 \times 2$ $= 20 ft³$
2. Convert to liters: 1 ft³ = 28.31684659 L
  $20 ft³ \times 28.31684659$ $= 566.336932 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{566.336932 L}{3.785411784}$ $= 149.61039 US gal$
9. Volume: 2.53 yd³
1. A cone holds one third of a cylinder with the same base and height, so take 1/3 × π × radius² × height
  $\frac{1}{3} \times π \times {1.1}^{2} \times 2$ $= 2.534218 yd³$
2. Convert to liters: 1 yd³ = 764.55485798 L
  $2.534218 yd³ \times 764.55485798$ $= 1,937.54874 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{1,937.54874 L}{3.785411784}$ $= 511.846227 US gal$
10. Volume: 1 mm³
1. A cube's length, width and height are all the same edge, so multiply the edge by itself three times
  $1^{3}$ $= 1 mm³$
2. Convert to liters: 1 mm³ = 0.000001 L
  $1 mm³ \times 0.000001$ $= 0.000001 L$
3. Convert to US gallons: 1 US gallon = 3.785411784 L
  $\frac{0.000001 L}{3.785411784}$ $= 2.641721e-7 US gal$