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Volume Concepts

Grade 5 · Geometry · Worksheet 3

  1. A rectangular prism-shaped fish tank has a length of 15.5 cm, a width of 8.2 cm, and a height of 12.4 cm. What is the volume of the fish tank in cubic centimeters?
    Answer: ______________
  2. Matiu is helping his family pack moving boxes. He has a large rectangular box that measures 600 millimeters long, 400 millimeters wide, and 300 millimeters tall. Matiu wants to fill the box completely with smaller cube-shaped gift boxes that each have a volume of 1,000 cubic millimeters. How many of these small gift boxes can Matiu fit inside the large box? Answer: ______________
  3. Charlotte is designing a rectangular prism-shaped jewelry box. The box has a length of 27 cm, a width of 12 cm, and a height of 7 cm. What is the volume of the jewelry box in cubic centimeters?
    Answer: ______________
  4. Emma is designing a rectangular fish tank for her classroom. The tank measures 2.4 meters in length, 1.2 meters in width, and 0.8 meters in height. If she fills the tank completely with water, how many cubic meters of water will the tank hold? Answer: ______________
  5. Mere is building a model of a storage shed using unit cubes. The shed has a length of 12 units, a width of 9 units, and a height of 10 units. What is the volume of the shed in cubic units? Answer: ______________
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Answer Key & Explanations

Volume Concepts · Grade 5 · Worksheet 3

  1. A rectangular prism-shaped fish tank has a length of 15.5 cm, a width of 8.2 cm, and a height of 12.4 cm. What is the volume of the fish tank in cubic centimeters? Answer: 1576.04 Solution: Write the volume formula for a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 15.5 × 8.2 × 12.4 First multiply 15.5 × 8.2 = 127.1 Then multiply 127.1 × 12.4 = 1576.04 The volume is 1576.04 cubic centimeters
    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 = 15.5 × 8.2 × 12.4 Step 3: First multiply 15.5 × 8.2 = 127.1 Step 4: Then multiply 127.1 × 12.4 = 1576.04 Step 5: The volume is 1576.04 cubic centimeters

  2. Matiu is helping his family pack moving boxes. He has a large rectangular box that measures 600 millimeters long, 400 millimeters wide, and 300 millimeters tall. Matiu wants to fill the box completely with smaller cube-shaped gift boxes that each have a volume of 1,000 cubic millimeters. How many of these small gift boxes can Matiu fit inside the large box? Answer: 72,000 Solution: Find the volume of the large rectangular box. Volume = length x width x height = 600 mm x 400 mm x 300 mm. Multiply the first two numbers: 600 x 400 = 240,000.
    Full step-by-step solution

    Step 1: Find the volume of the large rectangular box. Volume = length x width x height = 600 mm x 400 mm x 300 mm. Step 2: Multiply the first two numbers: 600 x 400 = 240,000. Step 3: Multiply the result by the height: 240,000 x 300 = 72,000,000 cubic millimeters. Step 4: Each small gift box has a volume of 1,000 cubic millimeters. To find how many fit, divide the large box's volume by the small box's volume: 72,000,000 / 1,000 = 72,000. The answer is 72,000 small gift boxes.

  3. Charlotte is designing a rectangular prism-shaped jewelry box. The box has a length of 27 cm, a width of 12 cm, and a height of 7 cm. What is the volume of the jewelry box in cubic centimeters? Answer: 2268 Solution: The volume of a rectangular prism is length times width times height. Find the area of the base: 27 cm times 12 cm = 324 square cm. This is how many unit cubes fit in one layer.
    Full step-by-step solution

    Step 1: The volume of a rectangular prism is length times width times height. Step 2: Find the area of the base: 27 cm times 12 cm = 324 square cm. This is how many unit cubes fit in one layer. Step 3: Multiply the base area by the height: 324 square cm times 7 cm = 2268 cubic cm. Step 4: The volume of the jewelry box is 2268 cubic centimeters.

  4. Emma is designing a rectangular fish tank for her classroom. The tank measures 2.4 meters in length, 1.2 meters in width, and 0.8 meters in height. If she fills the tank completely with water, how many cubic meters of water will the tank hold? Answer: 2.304 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given measurements: Volume = 2.4 × 1.2 × 0.8 Multiply the first two numbers: 2.4 × 1.2 = 2.88 Multiply the result by the height: 2.88 × 0.8 = 2.304 The volume is 2.304 cubic meters The answer…
    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 × 1.2 × 0.8 Step 3: Multiply the first two numbers: 2.4 × 1.2 = 2.88 Step 4: Multiply the result by the height: 2.88 × 0.8 = 2.304 Step 5: The volume is 2.304 cubic meters The answer is 2.304.

  5. Mere is building a model of a storage shed using unit cubes. The shed has a length of 12 units, a width of 9 units, and a height of 10 units. What is the volume of the shed in cubic units? Answer: 1080 Solution: The volume of a rectangular prism is found by multiplying length, width, and height: Volume = length x width x height. Substitute the given values: Volume = 12 x 9 x 10. First, multiply length and width: 12 x 9 = 108.
    Full step-by-step solution

    Step 1: The volume of a rectangular prism is found by multiplying length, width, and height: Volume = length x width x height. Step 2: Substitute the given values: Volume = 12 x 9 x 10. Step 3: First, multiply length and width: 12 x 9 = 108. This is the number of cubes in one layer. Step 4: Then, multiply by the height: 108 x 10 = 1080. Step 5: The volume of the shed is 1080 cubic units.