Measurement Conversion

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Answer Key & Explanations

Measurement Conversion · Grade 5 · Worksheet 3

1. A rectangular prism-shaped shipping container has a length of 2.5 meters, a width of 1.8 meters, and a height of 3.2 meters. What is the volume of the container in cubic centimeters? (Remember: 1 meter = 100 centimeters) Answer: 14400000 cubic centimeters Solution: Find the volume in cubic meters. The container is a rectangular prism, so its volume is length × width × height. Volume in cubic meters = 2.5 m × 1.8 m × 3.2 m.
   Full step-by-step solution

   Step 1: Find the volume in cubic meters. The container is a rectangular prism, so its volume is length × width × height. Volume in cubic meters = 2.5 m × 1.8 m × 3.2 m. Step 2: Multiply step by step. First: 2.5 × 1.8 = 4.5 Then: 4.5 × 3.2 = 14.4 So volume = 14.4 cubic meters. Step 3: Convert meters to centimeters for volume. 1 meter = 100 centimeters. 1 cubic meter = (100 cm) × (100 cm) × (100 cm) = 1,000,000 cubic centimeters. So to convert cubic meters to cubic centimeters, multiply by 1,000,000. Step 4: Apply the conversion. 14.4 cubic meters × 1,000,000 = 14,400,000 cubic centimeters. Step 5: Write the final answer. The volume of the container is 14,400,000 cubic centimeters.

2. A rectangular prism has a length of 12 cm, a width of 8 cm, and a height of 5 cm. What is the volume of this rectangular prism? Answer: 480 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Identify the given dimensions. Length = 12 cm Width = 8 cm Height = 5 cm Substitute the given numbers into the formula.
   Full step-by-step solution

   To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Identify the given dimensions. Length = 12 cm Width = 8 cm Height = 5 cm Step 2: Substitute the given numbers into the formula. Volume = 12 × 8 × 5 Step 3: Perform the multiplication step by step. First, multiply the length and the width: 12 × 8 = 96 Now, multiply this result by the height: 96 × 5 = 480 Step 4: State the final answer with the correct units. The volume is 480 cubic centimeters. Therefore, the volume of the rectangular prism is 480.

3. 12.5 × 3.6 = ? Answer: 45 Solution: Multiply the numbers as if they were whole numbers: 125 × 36 125 × 30 = 3750 125 × 6 = 750 Add the partial products: 3750 + 750 = 4500 Since 12.5 has one decimal place and 3.6 has one decimal place, the product must have two decimal places Place the decimal point: 4500 becomes 45.00, which…
   Full step-by-step solution

   Step 1: Multiply the numbers as if they were whole numbers: 125 × 36 Step 2: 125 × 30 = 3750 Step 3: 125 × 6 = 750 Step 4: Add the partial products: 3750 + 750 = 4500 Step 5: Since 12.5 has one decimal place and 3.6 has one decimal place, the product must have two decimal places Step 6: Place the decimal point: 4500 becomes 45.00, which simplifies to 45 Step 7: The answer is 45.

4. A rectangular prism-shaped shipping box has a length of 15.2 cm, a width of 9.8 cm, and a height of 6.5 cm. If you were to draw this box and calculate the total length of all its edges, what would be the total edge length in centimeters? Answer: 126 Solution: A rectangular prism has 12 edges total There are 4 edges of each dimension: 4 lengths, 4 widths, and 4 heights Calculate total length of all edges = (4 × length) + (4 × width) + (4 × height) Substitute the values: (4 × 15.2) + (4 × 9.8) + (4 × 6.5) Calculate each part: 4 × 15.2 = 60.8, 4 × 9.8 =…
   Full step-by-step solution

   Step 1: A rectangular prism has 12 edges total Step 2: There are 4 edges of each dimension: 4 lengths, 4 widths, and 4 heights Step 3: Calculate total length of all edges = (4 × length) + (4 × width) + (4 × height) Step 4: Substitute the values: (4 × 15.2) + (4 × 9.8) + (4 × 6.5) Step 5: Calculate each part: 4 × 15.2 = 60.8, 4 × 9.8 = 39.2, 4 × 6.5 = 26 Step 6: Add them together: 60.8 + 39.2 + 26 = 126 The answer is 126 cm.