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Fractional Volume

Grade 6 · Geometry · Worksheet 3

  1. Tane is helping his community build a rectangular planter box for a community garden. The planter box has a length of 12.5 feet, a width of 9.4 feet, and a height of 10.2 feet. He needs to order soil to fill the entire planter box. What is the volume of the planter box in cubic feet?
    Answer: ______________
  2. A shipping container has dimensions of 12.5 meters long, 2.4 meters wide, and 2.8 meters high. The company needs to know how many cubic meters of space are available for cargo. What is the volume of the shipping container in cubic meters? Answer: ______________
  3. (2/3) × (3/4) ÷ (1/2) = ? Answer: ______________
  4. Sophia is helping her family build a rectangular garden box for their backyard. The box has a length of 8.5 feet, a width of 4.75 feet, and a height of 2.5 feet. They plan to fill the box completely with soil. What is the volume of the garden box in cubic feet?
    Answer: ______________
  5. Hana is helping her family prepare a traditional Maori hangi. She is building a rectangular pit to hold the hot stones and food baskets. The pit needs to be 3.6 meters long, 2.4 meters wide, and 0.75 meters deep. What is the volume of the pit in cubic meters? Answer: ______________
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Answer Key & Explanations

Fractional Volume · Grade 6 · Worksheet 3

  1. Tane is helping his community build a rectangular planter box for a community garden. The planter box has a length of 12.5 feet, a width of 9.4 feet, and a height of 10.2 feet. He needs to order soil to fill the entire planter box. What is the volume of the planter box in cubic feet? Answer: 1198.5 Solution: The formula for the volume of a rectangular prism is V = l × w × h. Substitute the given dimensions: V = 12.5 × 9.4 × 10.2. First, multiply length by width: 12.5 × 9.4.
    Full step-by-step solution

    Step 1: The formula for the volume of a rectangular prism is V = l × w × h. Step 2: Substitute the given dimensions: V = 12.5 × 9.4 × 10.2. Step 3: First, multiply length by width: 12.5 × 9.4. 12.5 × 9 = 112.5 12.5 × 0.4 = 5.0 112.5 + 5.0 = 117.5 Step 4: Now multiply the result by the height: 117.5 × 10.2. 117.5 × 10 = 1175 117.5 × 0.2 = 23.5 1175 + 23.5 = 1198.5 Step 5: The volume of the planter box is 1198.5 cubic feet.

  2. A shipping container has dimensions of 12.5 meters long, 2.4 meters wide, and 2.8 meters high. The company needs to know how many cubic meters of space are available for cargo. What is the volume of the shipping container in cubic meters? Answer: 84 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 12.5 × 2.4 × 2.8 First multiply 12.5 × 2.4 = 30 Then multiply 30 × 2.8 = 84 The volume is 84 cubic meters.
    Full step-by-step solution

    Step 1: Identify the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 12.5 × 2.4 × 2.8 Step 3: First multiply 12.5 × 2.4 = 30 Step 4: Then multiply 30 × 2.8 = 84 Step 5: The volume is 84 cubic meters.

  3. (2/3) × (3/4) ÷ (1/2) = ? Answer: 1 Solution: Write the problem as given. (2/3) × (3/4) ÷ (1/2) Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, ÷ (1/2) = × (2/1).
    Full step-by-step solution

    Let's solve step-by-step. Step 1: Write the problem as given. (2/3) × (3/4) ÷ (1/2) Step 2: Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, ÷ (1/2) = × (2/1). Now the expression becomes: (2/3) × (3/4) × (2/1) Step 3: Multiply the fractions by multiplying all numerators together and all denominators together. Numerator: 2 × 3 × 2 = 12 Denominator: 3 × 4 × 1 = 12 Step 4: Write the result as a fraction: 12/12 Step 5: Simplify 12/12 = 1. Final answer: 1

  4. Sophia is helping her family build a rectangular garden box for their backyard. The box has a length of 8.5 feet, a width of 4.75 feet, and a height of 2.5 feet. They plan to fill the box completely with soil. What is the volume of the garden box in cubic feet? Answer: 100.9375 Solution: Use the formula for volume of a rectangular prism: Volume = length x width x height Substitute the given values: Volume = 8.5 x 4.75 x 2.5 Multiply length and width first: 8.5 x 4.75 = 40.375 Multiply the result by the height: 40.375 x 2.5 = 100.9375 The volume is 100.9375 cubic feet.
    Full step-by-step solution

    Step 1: Use the formula for volume of a rectangular prism: Volume = length x width x height Step 2: Substitute the given values: Volume = 8.5 x 4.75 x 2.5 Step 3: Multiply length and width first: 8.5 x 4.75 = 40.375 Step 4: Multiply the result by the height: 40.375 x 2.5 = 100.9375 Step 5: The volume is 100.9375 cubic feet.

  5. Hana is helping her family prepare a traditional Maori hangi. She is building a rectangular pit to hold the hot stones and food baskets. The pit needs to be 3.6 meters long, 2.4 meters wide, and 0.75 meters deep. What is the volume of the pit in cubic meters? Answer: 6.48 Solution: Use the formula for volume of a rectangular prism: Volume = length × width × height. Substitute the given values: Volume = 3.6 × 2.4 × 0.75. First multiply 3.6 × 2.4.
    Full step-by-step solution

    Step 1: Use the formula for volume of a rectangular prism: Volume = length × width × height. Step 2: Substitute the given values: Volume = 3.6 × 2.4 × 0.75. Step 3: First multiply 3.6 × 2.4. 3.6 × 2.4 = 8.64. Step 4: Then multiply 8.64 × 0.75. 8.64 × 0.75 = 6.48. Step 5: The volume is 6.48 cubic meters. The answer is 6.48.