Fractional Volume

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Answer Key & Explanations

Fractional Volume · Grade 6 · Worksheet 3

1. Liam is building a rectangular planter box for his garden. The box has a length of 2.5 meters, a width of 1.2 meters, and a height of 0.8 meters. He needs to fill it with soil, but the soil is sold in bags that each contain 0.5 cubic meters. How many full bags of soil does Liam need to buy to completely fill the planter box? Answer: 5 Solution: Volume = length × width × height Volume = 2.5 m × 1.2 m × 0.8 m First, multiply 2.5 and 1.2: 2.5 × 1.2 = 3.0 Now multiply by 0.8: 3.0 × 0.8 = 2.4 So, the volume of the box is 2.4 cubic meters.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Find the volume of the planter box** The box is a rectangular prism, so: Volume = length × width × height Volume = 2.5 m × 1.2 m × 0.8 m First, multiply 2.5 and 1.2: 2.5 × 1.2 = 3.0 Now multiply by 0.8: 3.0 × 0.8 = 2.4 So, the volume of the box is **2.4 cubic meters**. --- **Step 2: Determine how many bags are needed** Each bag contains 0.5 cubic meters of soil. Number of bags needed = Volume of box ÷ Volume per bag Number of bags = 2.4 ÷ 0.5 Dividing by 0.5 is the same as multiplying by 2: 2.4 × 2 = 4.8 So, 4.8 bags are needed. --- **Step 3: Decide on full bags** Since Liam can only buy full bags, he must round up to the nearest whole number. 4.8 → next whole number is **5**. --- **Step 4: Conclusion** Liam needs to buy **5 full bags** of soil to fill the planter box completely. --- **Final answer: 5**

2. Emma is designing a rectangular prism-shaped aquarium for her science project. The aquarium has a length of 2.4 meters, a width of 1.5 meters, and a height of 0.9 meters. She needs to fill it with water, but wants to leave 15% of the tank empty for air space and decorations. What volume of water, in cubic meters, should Emma put in the aquarium? Answer: 2.754 Solution: Volume = length × width × height Volume = 2.4 × 1.5 × 0.9 2.4 × 1.5 = 3.6 3.6 × 0.9 = 3.24 Total volume = 3.24 cubic meters Calculate the percentage of the tank that will be filled with water If 15% is empty, then 100% - 15% = 85% will be filled with water Water volume = 85% of total volume…
   Full step-by-step solution

   Step 1: Calculate the total volume of the aquarium Volume = length × width × height Volume = 2.4 × 1.5 × 0.9 2.4 × 1.5 = 3.6 3.6 × 0.9 = 3.24 Total volume = 3.24 cubic meters Step 2: Calculate the percentage of the tank that will be filled with water If 15% is empty, then 100% - 15% = 85% will be filled with water Step 3: Calculate the volume of water needed Water volume = 85% of total volume Water volume = 0.85 × 3.24 0.85 × 3.24 = 2.754 The answer is 2.754 cubic meters.

3. A shipping company is designing a new rectangular storage container. The container has a length of 3.2 meters, a width of 2.5 meters, and a height of 2.8 meters. Due to safety regulations, the container can only be filled to 85% of its total capacity. What is the maximum volume of goods, in cubic meters, that can be safely stored in this container? Answer: 19.04 Solution: Volume = length × width × height Volume = 3.2 × 2.5 × 2.8 3.2 × 2.5 = 8.0 8.0 × 2.8 = 22.4 Total volume = 22.4 cubic meters Calculate 85% of the total volume 85% = 85/100 = 0.85 Safe volume = 22.4 × 0.85 22.4 × 0.85 = 19.04 The maximum volume of goods that can be safely stored is 19.04 cubic meters.
   Full step-by-step solution

   Step 1: Calculate the total volume of the container Volume = length × width × height Volume = 3.2 × 2.5 × 2.8 Step 2: Multiply step by step 3.2 × 2.5 = 8.0 8.0 × 2.8 = 22.4 Total volume = 22.4 cubic meters Step 3: Calculate 85% of the total volume 85% = 85/100 = 0.85 Safe volume = 22.4 × 0.85 Step 4: Multiply to find the safe volume 22.4 × 0.85 = 19.04 The maximum volume of goods that can be safely stored is 19.04 cubic meters.