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Fractional Volume

Grade 6 · Geometry · Worksheet 2

  1. Kaia is designing a rectangular prism-shaped shipping crate for a sculpture. The crate's interior dimensions are 9.5 inches long, 7.25 inches wide, and 12.4 inches high. What is the volume of the crate in cubic inches? Answer: ______________
  2. Charlotte is helping her family build a new garden bed. The garden bed is a rectangular prism that measures 8.5 feet long, 3.2 feet wide, and 1.75 feet deep. Charlotte needs to buy enough soil to completely fill the garden bed. What is the volume of the garden bed in cubic feet? Answer: ______________
  3. A rectangular prism has dimensions 7 1/3 cm × 9 1/5 cm × 11 1/4 cm. What is its volume? Answer: ______________
  4. Charlotte is designing a rectangular prism-shaped storage box for her art supplies. The base of the box is a rectangle that measures 8.5 inches by 12.75 inches, and the box has a height of 10.4 inches. What is the volume of the storage box in cubic inches?
    Answer: ______________
  5. A rectangular prism has dimensions 3 1/4 cm × 5 1/2 cm × 7 3/4 cm. What is its volume? Answer: ______________
  6. (2 1/3 × 3 1/4 × 4 1/2) = ? Answer: ______________
  7. (2 1/4 × 3 1/3 × 4 1/2) = ? Answer: ______________
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Answer Key & Explanations

Fractional Volume · Grade 6 · Worksheet 2

  1. Kaia is designing a rectangular prism-shaped shipping crate for a sculpture. The crate's interior dimensions are 9.5 inches long, 7.25 inches wide, and 12.4 inches high. What is the volume of the crate in cubic inches? Answer: 854.05 Solution: Identify the dimensions: length = 9.5 in, width = 7.25 in, height = 12.4 in. Use the volume formula for a rectangular prism: V = l * w * h. Multiply length and width: 9.5 * 7.25 = 68.875.
    Full step-by-step solution

    Step 1: Identify the dimensions: length = 9.5 in, width = 7.25 in, height = 12.4 in. Step 2: Use the volume formula for a rectangular prism: V = l * w * h. Step 3: Multiply length and width: 9.5 * 7.25 = 68.875. Step 4: Multiply the result by height: 68.875 * 12.4. Step 5: Calculate 68.875 * 12.4 = 68.875 * (12 + 0.4) = 68.875 * 12 + 68.875 * 0.4 = 826.5 + 27.55 = 854.05. Step 6: The volume is 854.05 cubic inches. The answer is 854.05.

  2. Charlotte is helping her family build a new garden bed. The garden bed is a rectangular prism that measures 8.5 feet long, 3.2 feet wide, and 1.75 feet deep. Charlotte needs to buy enough soil to completely fill the garden bed. What is the volume of the garden bed in cubic feet? Answer: 47.6 Solution: Write down the formula for volume of a rectangular prism: V = l × w × h Substitute the given values: V = 8.5 × 3.2 × 1.75 First multiply 8.5 × 3.2: 8.5 × 3.2 = 27.2 Then multiply 27.2 × 1.75: 27.2 × 1.75 = 47.6 The volume of the garden bed is 47.6 cubic feet.
    Full step-by-step solution

    Step 1: Write down the formula for volume of a rectangular prism: V = l × w × h Step 2: Substitute the given values: V = 8.5 × 3.2 × 1.75 Step 3: First multiply 8.5 × 3.2: 8.5 × 3.2 = 27.2 Step 4: Then multiply 27.2 × 1.75: 27.2 × 1.75 = 47.6 Step 5: The volume of the garden bed is 47.6 cubic feet. The answer is 47.6.

  3. A rectangular prism has dimensions 7 1/3 cm × 9 1/5 cm × 11 1/4 cm. What is its volume? Answer: 759 cm³ Solution: Convert each mixed number to an improper fraction. 7 1/3 = (7 × 3 + 1)/3 = 22/3 9 1/5 = (9 × 5 + 1)/5 = 46/5 11 1/4 = (11 × 4 + 1)/4 = 45/4 Multiply the three fractions.
    Full step-by-step solution

    Step 1: Convert each mixed number to an improper fraction. 7 1/3 = (7 × 3 + 1)/3 = 22/3 9 1/5 = (9 × 5 + 1)/5 = 46/5 11 1/4 = (11 × 4 + 1)/4 = 45/4 Step 2: Multiply the three fractions. (22/3) × (46/5) × (45/4) = (22 × 46 × 45) / (3 × 5 × 4) Step 3: Multiply the numerators. 22 × 46 = 1012 1012 × 45 = 1012 × (40 + 5) = 40480 + 5060 = 45540 So numerator = 45540 Step 4: Multiply the denominators. 3 × 5 = 15 15 × 4 = 60 So denominator = 60 Step 5: Write the fraction and simplify. 45540/60 Divide numerator and denominator by 10: 4554/6 Divide numerator and denominator by 6: 4554 ÷ 6 = 759, 6 ÷ 6 = 1 So 45540/60 = 759/1 = 759 The answer is 759 cm³.

  4. Charlotte is designing a rectangular prism-shaped storage box for her art supplies. The base of the box is a rectangle that measures 8.5 inches by 12.75 inches, and the box has a height of 10.4 inches. What is the volume of the storage box in cubic inches? Answer: 1127.1 Solution: Identify the dimensions of the rectangular prism. Length = 12.75 inches Width = 8.5 inches Height = 10.4 inches Use the formula for volume of a rectangular prism: V = l × w × h Multiply the length and width first.
    Full step-by-step solution

    Step 1: Identify the dimensions of the rectangular prism. Length = 12.75 inches Width = 8.5 inches Height = 10.4 inches Step 2: Use the formula for volume of a rectangular prism: V = l × w × h Step 3: Multiply the length and width first. 12.75 × 8.5 = 108.375 square inches (area of the base) Step 4: Multiply the base area by the height. 108.375 × 10.4 = 1127.1 cubic inches Step 5: Verify by multiplying in a different order. 12.75 × 10.4 = 132.6 132.6 × 8.5 = 1127.1 cubic inches The answer is 1127.1 cubic inches.

  5. A rectangular prism has dimensions 3 1/4 cm × 5 1/2 cm × 7 3/4 cm. What is its volume? Answer: 138 21/32 cm³ Solution: Convert 3 1/4 to an improper fraction: (3 × 4 + 1)/4 = 13/4 Convert 5 1/2 to an improper fraction: (5 × 2 + 1)/2 = 11/2 Convert 7 3/4 to an improper fraction: (7 × 4 + 3)/4 = 31/4 Multiply the three fractions: (13/4) × (11/2) × (31/4) = (13 × 11 × 31)/(4 × 2 × 4) Multiply the numerators: 13 × 11…
    Full step-by-step solution

    Step 1: Convert 3 1/4 to an improper fraction: (3 × 4 + 1)/4 = 13/4 Step 2: Convert 5 1/2 to an improper fraction: (5 × 2 + 1)/2 = 11/2 Step 3: Convert 7 3/4 to an improper fraction: (7 × 4 + 3)/4 = 31/4 Step 4: Multiply the three fractions: (13/4) × (11/2) × (31/4) = (13 × 11 × 31)/(4 × 2 × 4) Step 5: Multiply the numerators: 13 × 11 = 143, 143 × 31 = 4433 Step 6: Multiply the denominators: 4 × 2 = 8, 8 × 4 = 32 Step 7: The fraction is 4433/32 Step 8: Convert to a mixed number: 4433 ÷ 32 = 138 remainder 21, so 138 21/32 Step 9: Add the units: cm³ The volume is 138 21/32 cm³.

  6. (2 1/3 × 3 1/4 × 4 1/2) = ? Answer: 34 1/8 Solution: Convert 2 1/3 to an improper fraction: (2 × 3 + 1)/3 = 7/3 Convert 3 1/4 to an improper fraction: (3 × 4 + 1)/4 = 13/4 Convert 4 1/2 to an improper fraction: (4 × 2 + 1)/2 = 9/2 Multiply the fractions: (7/3) × (13/4) × (9/2) Multiply numerators: 7 × 13 × 9 = 819 Multiply denominators: 3 × 4 × 2…
    Full step-by-step solution

    Step 1: Convert 2 1/3 to an improper fraction: (2 × 3 + 1)/3 = 7/3 Step 2: Convert 3 1/4 to an improper fraction: (3 × 4 + 1)/4 = 13/4 Step 3: Convert 4 1/2 to an improper fraction: (4 × 2 + 1)/2 = 9/2 Step 4: Multiply the fractions: (7/3) × (13/4) × (9/2) Step 5: Multiply numerators: 7 × 13 × 9 = 819 Step 6: Multiply denominators: 3 × 4 × 2 = 24 Step 7: Simplify 819/24: 819 ÷ 3 = 273, 24 ÷ 3 = 8, so we get 273/8 Step 8: Convert 273/8 to a mixed number: 273 ÷ 8 = 34 with remainder 1, so 34 1/8 Step 9: The volume is 34 1/8 cubic units

  7. (2 1/4 × 3 1/3 × 4 1/2) = ? Answer: 33 3/4 Solution: Convert 2 1/4 to an improper fraction: (2 × 4 + 1)/4 = 9/4 Convert 3 1/3 to an improper fraction: (3 × 3 + 1)/3 = 10/3 Convert 4 1/2 to an improper fraction: (4 × 2 + 1)/2 = 9/2 Multiply the fractions: (9/4) × (10/3) × (9/2) Multiply numerators: 9 × 10 × 9 = 810 Multiply denominators: 4 × 3 × 2…
    Full step-by-step solution

    Step 1: Convert 2 1/4 to an improper fraction: (2 × 4 + 1)/4 = 9/4 Step 2: Convert 3 1/3 to an improper fraction: (3 × 3 + 1)/3 = 10/3 Step 3: Convert 4 1/2 to an improper fraction: (4 × 2 + 1)/2 = 9/2 Step 4: Multiply the fractions: (9/4) × (10/3) × (9/2) Step 5: Multiply numerators: 9 × 10 × 9 = 810 Step 6: Multiply denominators: 4 × 3 × 2 = 24 Step 7: Simplify 810/24: divide numerator and denominator by 6 = 135/4 Step 8: Convert 135/4 to mixed number: 135 ÷ 4 = 33 with remainder 3, so 33 3/4 The answer is 33 3/4.