Volume Concepts

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Answer Key & Explanations

Volume Concepts · Grade 5 · Worksheet 2

1. (20 × 15 × 8) ÷ 4 = ? Answer: 600 Solution: Calculate 20 × 15 = 300 Multiply the result by 8: 300 × 8 = 2400 Divide by 4: 2400 ÷ 4 = 600 The answer is 600.
   Full step-by-step solution

   Step 1: Calculate 20 × 15 = 300 Step 2: Multiply the result by 8: 300 × 8 = 2400 Step 3: Divide by 4: 2400 ÷ 4 = 600 The answer is 600.

2. A fish tank in the shape of a rectangular prism has a length of 8.25 feet, a width of 3.4 feet, and a height of 2.75 feet. What is the volume of the fish tank in cubic feet? Answer: 77.1375 Solution: Write the volume formula for a rectangular prism: Volume = length × width × height Substitute the given measurements: Volume = 8.25 × 3.4 × 2.75 First multiply 8.25 × 3.4 8.25 × 3.4 = 28.05 Now multiply the result by the height: 28.05 × 2.75 28.05 × 2.75 = 77.1375 The volume of the fish tank is…
   Full step-by-step solution

   Step 1: Write the volume formula for a rectangular prism: Volume = length × width × height Step 2: Substitute the given measurements: Volume = 8.25 × 3.4 × 2.75 Step 3: First multiply 8.25 × 3.4 8.25 × 3.4 = 28.05 Step 4: Now multiply the result by the height: 28.05 × 2.75 28.05 × 2.75 = 77.1375 Step 5: The volume of the fish tank is 77.1375 cubic feet.

3. A fish tank in the shape of a rectangular prism has a length of 8.75 feet, a width of 3.2 feet, and a height of 4.5 feet. What is the volume of the fish tank in cubic feet? Answer: 126 Solution: Write the volume formula for a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 8.75 × 3.2 × 4.5 First multiply 8.75 × 3.2 8.75 × 3 = 26.25 8.75 × 0.2 = 1.75 26.25 + 1.75 = 28 So 8.75 × 3.2 = 28 Now multiply 28 × 4.5 28 × 4 = 112 28 × 0.5 = 14 112 + 14 =…
   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 = 8.75 × 3.2 × 4.5 Step 3: First multiply 8.75 × 3.2 8.75 × 3 = 26.25 8.75 × 0.2 = 1.75 26.25 + 1.75 = 28 So 8.75 × 3.2 = 28 Step 4: Now multiply 28 × 4.5 28 × 4 = 112 28 × 0.5 = 14 112 + 14 = 126 Step 5: The volume is 126 cubic feet The answer is 126.

4. ∛2744 = ? Answer: 14 Solution: We need to find the cube root of 2744, which means finding a number that when multiplied by itself three times equals 2744.
   Full step-by-step solution

   Step 1: We need to find the cube root of 2744, which means finding a number that when multiplied by itself three times equals 2744. Step 2: Try 10: 10 × 10 × 10 = 1000 (too small) Step 3: Try 12: 12 × 12 × 12 = 144 × 12 = 1728 (still too small) Step 4: Try 14: 14 × 14 × 14 = 196 × 14 = 2744 Step 5: Since 14 × 14 × 14 = 2744, the cube root of 2744 is 14. The answer is 14.

5. (20 × 15 × 8) ÷ 2 = ? Answer: 1200 Solution: Multiply 20 × 15 = 300 Multiply 300 × 8 = 2400 Divide 2400 ÷ 2 = 1200 The answer is 1200.
   Full step-by-step solution

   Step 1: Multiply 20 × 15 = 300 Step 2: Multiply 300 × 8 = 2400 Step 3: Divide 2400 ÷ 2 = 1200 The answer is 1200.

6. (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.