Fractional Volume

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Answer Key & Explanations

Fractional Volume · Grade 6 · Worksheet 1

1. Mason is helping his uncle build a custom rectangular aquarium for a local pet store. The aquarium needs to have a length of 8.5 feet, a width of 3.2 feet, and a height of 2.75 feet. The store wants to know exactly how much water the tank can hold when completely full. What is the volume of the aquarium in cubic feet? Answer: 74.8 Solution: Use the formula for volume of a rectangular prism: V = l × w × h Substitute the given values: V = 8.5 × 3.2 × 2.75 Multiply the first two numbers: 8.5 × 3.2 = 27.2 Multiply the result by the height: 27.2 × 2.75 Calculate 27.2 × 2.75: 27.2 × 2 = 54.4, and 27.2 × 0.75 = 20.4, so 54.4 + 20.4 = 74.8…
   Full step-by-step solution

   Step 1: Use the formula for volume of a rectangular prism: V = l × w × h Step 2: Substitute the given values: V = 8.5 × 3.2 × 2.75 Step 3: Multiply the first two numbers: 8.5 × 3.2 = 27.2 Step 4: Multiply the result by the height: 27.2 × 2.75 Step 5: Calculate 27.2 × 2.75: 27.2 × 2 = 54.4, and 27.2 × 0.75 = 20.4, so 54.4 + 20.4 = 74.8 Step 6: The volume is 74.8 cubic feet. The answer is 74.8.

2. Noah is helping his aunt build a custom rectangular storage chest for her art studio. The interior of the chest must have a length of 8.4 feet, a width of 3.5 feet, and a height of 2.75 feet. He needs to calculate the total interior volume to ensure it will hold all her large canvases and supplies. What is the volume of the storage chest in cubic feet? Answer: 80.85 Solution: Use the formula for volume of a rectangular prism: V = l × w × h Substitute the given dimensions: V = 8.4 × 3.5 × 2.75 First multiply length and width: 8.4 × 3.5 = 29.4 Then multiply the result by the height: 29.4 × 2.75 Multiply 29.4 × 2.75: 29.4 × 2 = 58.8, 29.4 × 0.75 = 22.05, then add: 58.8…
   Full step-by-step solution

   Step 1: Use the formula for volume of a rectangular prism: V = l × w × h Step 2: Substitute the given dimensions: V = 8.4 × 3.5 × 2.75 Step 3: First multiply length and width: 8.4 × 3.5 = 29.4 Step 4: Then multiply the result by the height: 29.4 × 2.75 Step 5: Multiply 29.4 × 2.75: 29.4 × 2 = 58.8, 29.4 × 0.75 = 22.05, then add: 58.8 + 22.05 = 80.85 Step 6: The volume is 80.85 cubic feet.

3. Kaia is helping her family build a custom rectangular sandbox for her younger cousins. The sandbox has a length of 3.5 meters, a width of 1.5 meters, and a height of 0.9 meters. Her father wants to know exactly how much sand, in cubic meters, they will need to fill the sandbox completely. What is the volume of the sandbox in cubic meters? Answer: 4.725 Solution: The formula for the volume of a rectangular prism is Volume = length × width × height. Substitute the given dimensions: length = 3.5 m, width = 1.5 m, height = 0.9 m.
   Full step-by-step solution

   Step 1: The formula for the volume of a rectangular prism is Volume = length × width × height. Step 2: Substitute the given dimensions: length = 3.5 m, width = 1.5 m, height = 0.9 m. Step 3: First, multiply the length by the width: 3.5 × 1.5 = 5.25. Step 4: Then, multiply that result by the height: 5.25 × 0.9 = 4.725. Step 5: The volume is 4.725 cubic meters. The answer is 4.725.