Rectangular Prism Volume

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Answer Key & Explanations

Rectangular Prism Volume · Grade 5 · Worksheet 3

1. Charlotte is helping her teacher organize a shipment of new books for the school library. The books are packed in large rectangular boxes that measure 18 inches long, 12 inches wide, and 10 inches tall. What is the volume of one of these boxes in cubic inches? Answer: 2160 Solution: Recall the formula for the volume of a rectangular prism: Volume = length × width × height. Identify the dimensions from the problem: length = 18 inches, width = 12 inches, height = 10 inches.
   Full step-by-step solution

   Step 1: Recall the formula for the volume of a rectangular prism: Volume = length × width × height. Step 2: Identify the dimensions from the problem: length = 18 inches, width = 12 inches, height = 10 inches. Step 3: Multiply the length and width: 18 × 12 = 216. Step 4: Multiply the result by the height: 216 × 10 = 2160. Step 5: The volume of the box is 2160 cubic inches.

2. Emma is packing books into a rectangular storage bin. The bin is 9 inches long, 7 inches wide, and 5 inches tall. What is the volume of the storage bin in cubic inches? Answer: 315 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height. Write down the measurements from the problem: length = 9 inches, width = 7 inches, height = 5 inches.
   Full step-by-step solution

   Step 1: Identify the formula for volume of a rectangular prism: Volume = length × width × height. Step 2: Write down the measurements from the problem: length = 9 inches, width = 7 inches, height = 5 inches. Step 3: Multiply the length and width: 9 × 7 = 63. Step 4: Multiply the result by the height: 63 × 5 = 315. Step 5: The volume is 315 cubic inches.

3. 6 × 4 × 5 = ? Answer: 120 Solution: Multiply the first two numbers: 6 × 4 = 24 Multiply the result by the third number: 24 × 5 = 120 The answer is 120.
   Full step-by-step solution

   Step 1: Multiply the first two numbers: 6 × 4 = 24 Step 2: Multiply the result by the third number: 24 × 5 = 120 The answer is 120.

4. Maya is designing a rectangular fish tank for her classroom. The tank needs to be 2.4 meters long, 1.5 meters wide, and hold water to a depth of 0.8 meters. What is the volume of water, in cubic meters, that the tank will hold when filled? Answer: 2.88 Solution: Identify the formula for the volume of a rectangular prism: Volume = length × width × height. Substitute the given measurements into the formula: Volume = 2.4 m × 1.5 m × 0.8 m.
   Full step-by-step solution

   Step 1: Identify the formula for the volume of a rectangular prism: Volume = length × width × height. Step 2: Substitute the given measurements into the formula: Volume = 2.4 m × 1.5 m × 0.8 m. Step 3: First, multiply the length and width: 2.4 × 1.5 = 3.6. Step 4: Now multiply that result by the height: 3.6 × 0.8 = 2.88. Step 5: The volume is 2.88 cubic meters.

5. A rectangular prism-shaped shipping container has a length of 12.4 meters, a width of 3.6 meters, and a height of 2.9 meters. What is the volume of this container in cubic meters? Answer: 129.456 Solution: Write the volume formula for a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 12.4 × 3.6 × 2.9 First multiply 12.4 × 3.6 12.4 × 3 = 37.2 12.4 × 0.6 = 7.44 37.2 + 7.44 = 44.64 Now multiply 44.64 × 2.9 44.64 × 2 = 89.28 44.64 × 0.9 = 40.176 89.28 + 40.176…
   Full step-by-step solution

   Step 1: Write the volume formula for a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 12.4 × 3.6 × 2.9 Step 3: First multiply 12.4 × 3.6 12.4 × 3 = 37.2 12.4 × 0.6 = 7.44 37.2 + 7.44 = 44.64 Step 4: Now multiply 44.64 × 2.9 44.64 × 2 = 89.28 44.64 × 0.9 = 40.176 89.28 + 40.176 = 129.456 Step 5: The volume is 129.456 cubic meters

6. Olivia is helping her neighbor build a rectangular garden bed. The bed needs to be 15 feet long, 10 feet wide, and 5 feet deep. What is the volume of soil, in cubic feet, needed to fill the garden bed completely? Answer: 750 Solution: Use the formula for the volume of a rectangular prism: Volume = length x width x height. Write down the measurements from the problem: length = 15 feet, width = 10 feet, height (depth) = 5 feet.
   Full step-by-step solution

   Step 1: Use the formula for the volume of a rectangular prism: Volume = length x width x height. Step 2: Write down the measurements from the problem: length = 15 feet, width = 10 feet, height (depth) = 5 feet. Step 3: Multiply the length and width: 15 x 10 = 150. Step 4: Multiply that result by the height: 150 x 5 = 750. Step 5: The volume is 750 cubic feet. The answer is 750.

7. Liam is building a wooden storage box for his art supplies. The box is 2.5 feet long, 1.8 feet wide, and 1.2 feet high. What is the volume of the storage box in cubic feet? Answer: 5.4 Solution: To find the volume of a rectangular box, we use the formula: Volume = length × width × height Length = 2.5 feet Width = 1.8 feet Height = 1.2 feet 2.5 × 1.8 = 4.5 4.5 × 1.2 = 5.4 The volume is 5.4 cubic feet.
   Full step-by-step solution

   To find the volume of a rectangular box, we use the formula: Volume = length × width × height Step 1: Write down the given dimensions: Length = 2.5 feet Width = 1.8 feet Height = 1.2 feet Step 2: Multiply the length and width first: 2.5 × 1.8 = 4.5 Step 3: Multiply the result by the height: 4.5 × 1.2 = 5.4 Step 4: Include the units: The volume is 5.4 cubic feet. Final Answer: 5.4