Calculate Volume: 30m × 15m × 5m Swimming Pool Dimensions

Volume Calculation with Rectangular Pool Dimensions

Gus builds a swimming pool 30 m long, 5 m deep, and 15 m wide. What is its volume?

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Step-by-step written solution

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1

Understand the problem

Gus builds a swimming pool 30 m long, 5 m deep, and 15 m wide. What is its volume?

2

Step-by-step solution

To solve this problem, we'll calculate the volume of the swimming pool using the formula for the volume of a rectangular prism.

  • Step 1: Identify the given dimensions of the swimming pool:
    • Length (L L ) = 30 m
    • Width (W W ) = 15 m
    • Height (H H ) = 5 m
  • Step 2: Use the formula for the volume of a rectangular prism:
    • V=L×W×H V = L \times W \times H
  • Step 3: Substitute the given values into the formula:
    • V=30×15×5 V = 30 \times 15 \times 5
  • Step 4: Perform the calculations:
    • First, calculate 30×15=450 30 \times 15 = 450
    • Then, multiply the intermediate result by the height: 450×5=2250 450 \times 5 = 2250

Therefore, the volume of Gus's swimming pool is 2250 m3 2250~m^3 .

3

Final Answer

2250 m3 2250~m^3

Key Points to Remember

Essential concepts to master this topic
  • Formula: Volume of rectangular prism equals length times width times height
  • Technique: Multiply step by step: 30 × 15 = 450, then 450 × 5 = 2250
  • Check: Units should be cubic meters (m³) and answer makes sense for pool size ✓

Common Mistakes

Avoid these frequent errors
  • Adding dimensions instead of multiplying
    Don't add 30 + 15 + 5 = 50 m³! This gives the perimeter concept, not volume. Volume requires space in three dimensions. Always multiply all three dimensions: length × width × height.

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FAQ

Everything you need to know about this question

Why do we multiply the dimensions instead of adding them?

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Volume measures space inside a 3D object. Adding gives you a perimeter (around the edges), but multiplying length × width × height gives you the cubic space that can hold water.

What does m³ mean and why is it important?

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m³ means cubic meters - it shows we're measuring volume (3D space). Always include cubic units for volume problems. If you forget the ³, your answer looks like area instead of volume!

Can I multiply the dimensions in any order?

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Yes! Multiplication is commutative, so 30 × 15 × 5 = 15 × 5 × 30 = 5 × 30 × 15. All give the same answer: 2250 m³.

How do I know if 2250 m³ is reasonable for a swimming pool?

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Think about it: this pool is 30m long (about 3 houses), 15m wide (very wide!), and 5m deep (deeper than most pools). So 2250 m³ is reasonable for such a large pool.

What if the problem gave different units like feet or centimeters?

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The same formula works: length × width × height. Just make sure all dimensions use the same units before multiplying. Your final answer will be in cubic units of whatever you used.

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