Volume Concepts

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Answer Key & Explanations

Volume Concepts · Grade 5 · Worksheet 2

1. Sophia is helping her school's art club build a storage box for clay sculptures. The box is a rectangular prism that measures 1.6 meters long, 1.1 meters wide, and 0.6 meters high. What is the volume of the storage box in cubic meters? Answer: 1.056 Solution: Identify the dimensions: length = 1.6 m, width = 1.1 m, height = 0.6 m. Step 2: Use the formula for volume of a rectangular prism: Volume = length × width × height. Step 3: Multiply length by width: 1.6 × 1.1 = 1.76.
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 1.6 m, width = 1.1 m, height = 0.6 m. Step 2: Use the formula for volume of a rectangular prism: Volume = length × width × height. Step 3: Multiply length by width: 1.6 × 1.1 = 1.76. Step 4: Multiply the result by the height: 1.76 × 0.6 = 1.056. Step 5: The volume is 1.056 cubic meters.

2. ∛729 = ? Answer: 9 Solution: We are looking for a number that, when multiplied by itself three times, equals 729. Since 9 × 9 × 9 = 729, the cube root of 729 is 9.
   Full step-by-step solution

   Step 1: We are looking for a number that, when multiplied by itself three times, equals 729. Step 2: Let's test 9: 9 × 9 = 81, and 81 × 9 = 729. Step 3: Since 9 × 9 × 9 = 729, the cube root of 729 is 9. The answer is 9.

3. Liam is building a rectangular planter box for his garden. The box measures 1.5 meters long, 0.8 meters wide, and 0.6 meters high. If he fills the box completely with soil, how many cubic meters of soil will he need? Answer: 0.72 Solution: To find the amount of soil needed, we need to calculate the volume of the rectangular planter box. The formula for the volume of a rectangular box is: Volume = length × width × height Length = 1.5 meters Width = 0.8 meters Height = 0.6 meters 1.5 × 0.8 = 1.2 1.2 × 0.6 = 0.72 Volume = 0.72 cubic…
   Full step-by-step solution

   To find the amount of soil needed, we need to calculate the volume of the rectangular planter box. The formula for the volume of a rectangular box is: Volume = length × width × height Step 1: Write down the given dimensions: Length = 1.5 meters Width = 0.8 meters Height = 0.6 meters Step 2: Multiply the length and width first: 1.5 × 0.8 = 1.2 Step 3: Multiply the result by the height: 1.2 × 0.6 = 0.72 Step 4: Include the unit for volume: Volume = 0.72 cubic meters So, Liam will need 0.72 cubic meters of soil to fill the box completely.

4. A rectangular prism has a length of 12 cm, width of 8 cm, and height of 5 cm. What is the volume of this prism? Answer: 480 Solution: The formula for volume of a rectangular prism is length × width × height Multiply the length and width: 12 × 8 = 96 Multiply this result by the height: 96 × 5 = 480 Include the units: 480 cubic centimeters The volume is 480 cm³.
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height Step 2: Multiply the length and width: 12 × 8 = 96 Step 3: Multiply this result by the height: 96 × 5 = 480 Step 4: Include the units: 480 cubic centimeters The volume is 480 cm³.

5. Mason is helping his family move and needs to pack a rectangular storage bin. The bin measures 1.8 meters in length, 1.2 meters in width, and 0.9 meters in height. What is the volume of the storage bin in cubic meters? Answer: 1.944 Solution: Identify the dimensions: length = 1.8 m, width = 1.2 m, height = 0.9 m. Step 2: Use the volume formula for a rectangular prism: Volume = length x width x height. Step 3: Multiply the first two numbers: 1.8 x 1.2 = 2.16.
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 1.8 m, width = 1.2 m, height = 0.9 m. Step 2: Use the volume formula for a rectangular prism: Volume = length x width x height. Step 3: Multiply the first two numbers: 1.8 x 1.2 = 2.16. Step 4: Multiply the result by the height: 2.16 x 0.9 = 1.944. Step 5: The volume of the storage bin is 1.944 cubic meters.

6. A shipping company is packing boxes into a large container. The container is shaped like a rectangular prism that measures 2.4 meters long, 1.8 meters wide, and 1.5 meters high. What is the volume of the container in cubic meters? Answer: 6.48 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given measurements: Volume = 2.4 × 1.8 × 1.5 First multiply 2.4 × 1.8 = 4.32 Then multiply 4.32 × 1.5 = 6.48 The volume is 6.48 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 measurements: Volume = 2.4 × 1.8 × 1.5 Step 3: First multiply 2.4 × 1.8 = 4.32 Step 4: Then multiply 4.32 × 1.5 = 6.48 Step 5: The volume is 6.48 cubic meters

7. (15 × 8 × 6) ÷ 3 = ? Answer: 240 Solution: Multiply the numbers inside the parentheses: 15 × 8 = 120 Multiply the result by the third number: 120 × 6 = 720 Divide the product by the number outside the parentheses: 720 ÷ 3 = 240 The answer is 240.
   Full step-by-step solution

   Step 1: Multiply the numbers inside the parentheses: 15 × 8 = 120 Step 2: Multiply the result by the third number: 120 × 6 = 720 Step 3: Divide the product by the number outside the parentheses: 720 ÷ 3 = 240 The answer is 240.