Calculate Total Pool Volume: 180 m³ is 40% of What?

Percentage Problems with Volume Calculations

A pool was filled with water over the course of two days:

If on the first day, the pool was filled with 180 m3 m^3 of water constituting 40%.

What is the total amount of water used to fill the pool?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the amount of water filled in two days
00:08 Convert percentages to fractions
00:25 Break down 40 into factors 2 and 20
00:29 Break down 100 into factors 5 and 20
00:35 Simplify wherever possible
00:53 This is the percentage of the total amount
00:59 Mark this amount as unknown X
01:06 Write the equation and solve for X
01:09 Isolate X
01:38 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A pool was filled with water over the course of two days:

If on the first day, the pool was filled with 180 m3 m^3 of water constituting 40%.

What is the total amount of water used to fill the pool?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information.
  • Step 2: Use the appropriate formula to determine the total capacity of the pool.
  • Step 3: Perform the necessary calculations to find the answer.

Now, let's work through each step:

Step 1: We are informed that 40% of the pool's capacity is filled with 180 m3 m^3 of water.
This means that 40% of the pool's total capacity equals 180 m3 m^3 .

Step 2: To find the total capacity (denoted by T T ), use the percentage formula:
T=Percentage value(Percentage100) T = \frac{\text{Percentage value}}{\left( \frac{\text{Percentage}}{100} \right)}

Step 3: Substitute the known values into the formula:
T=180(40100) T = \frac{180}{\left( \frac{40}{100} \right)}

This simplifies to:
T=1800.4=450 T = \frac{180}{0.4} = 450

Therefore, the total capacity of the pool is 450 m3 m^3 .

3

Final Answer

450 m³

Key Points to Remember

Essential concepts to master this topic
  • Formula: Total = Part ÷ Percentage (as decimal)
  • Technique: Convert 40% to 0.4, then 180 ÷ 0.4 = 450
  • Check: Verify 40% of 450 = 180 m³ ✓

Common Mistakes

Avoid these frequent errors
  • Using percentage as whole number in division
    Don't divide 180 ÷ 40 = 4.5 m³! This treats percentage as a whole number instead of a decimal. The result is way too small for a pool. Always convert percentage to decimal first: 40% = 0.4, then divide 180 ÷ 0.4 = 450 m³.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why do I divide by 0.4 instead of multiply by 40%?

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When you know the part and need the whole, you divide! Think of it this way: if 40% equals 180, then 100% equals how much? Use the formula: Total=PartPercentage as decimal \text{Total} = \frac{\text{Part}}{\text{Percentage as decimal}}

How do I convert percentages to decimals quickly?

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Simply move the decimal point two places left! For example: 40% becomes 0.40 or 0.4, and 25% becomes 0.25. This works because percent means 'per hundred'.

What if I get confused about which number is the part and which is the whole?

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Look for key words! The problem says '180 m³ constituting 40%' - this tells you 180 is the part (40% of something), and you need to find the whole (total capacity).

Can I solve this using proportions instead?

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Yes! Set up the proportion: 180x=40100 \frac{180}{x} = \frac{40}{100} , then cross-multiply: 40x = 18,000, so x = 450 m³. Both methods give the same answer!

How do I check if 450 m³ is reasonable for a pool?

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Think about it logically: if 180 m³ is only 40% of the pool, the total should be more than double that amount. Since 450 > 360 (double of 180), this makes sense!

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