/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 79 A can of paint holds 120 L. How ... [FREE SOLUTION] | 91影视

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Chapter 8: Problem 79

A can of paint holds 120 L. How many kiloliters are contained in 8 cans?

Short Answer

Expert verified
0.96 kL

Step by step solution

01

- Understand the Conversion

1 kiloliter (kL) is equal to 1000 liters (L). This is the basic unit conversion needed to solve the problem.
02

- Calculate the Total Volume in Liters

First, find the total volume of paint in all 8 cans. Since each can holds 120 liters, multiply the volume of one can by the number of cans: \[ 120 \text{ L/can} \times 8 \text{ cans} = 960 \text{ L} \]
03

- Convert Liters to Kiloliters

Convert the total volume from liters to kiloliters. Since 1 kiloliter is 1000 liters, divide the total volume in liters by 1000: \[ 960 \text{ L} \times \frac{1 \text{ kL}}{1000 \text{ L}} = 0.96 \text{ kL} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Liters to Kiloliters Conversion
Understanding how to convert liters (L) to kiloliters (kL) is essential for many real-world applications. Here's the basic concept:
- 1 kiloliter (kL) is equal to 1000 liters (L)
This means that if you have a certain number of liters, you can convert it to kiloliters by dividing the number of liters by 1000.
For example, if you have 2000 liters of water, you can convert it to kiloliters by using the following calculation:
\( 2000 \text{ L} \times \frac{1 \text{ kL}}{1000 \text{ L}} = 2 \text{ kL} \)
Knowing this simple conversion is highly beneficial when dealing with large volumes of liquid, as it can make the numbers more manageable and easier to understand.
Multiplication for Total Volume
Often, you need to find the total volume of multiple containers. This requires simple multiplication.
Let's consider the example from the exercise:
Each can of paint holds 120 liters, and we have 8 cans in total.
To find the total volume, you multiply the volume of one can by the number of cans:
\( 120 \text{ L/can} \times 8 \text{ cans} = 960 \text{ L} \)
This tells us that there are 960 liters in total.
This method can be applied to any number of containers to quickly find the cumulative volume.
  • Step 1: Identify the volume of one container.
  • Step 2: Multiply that volume by the total number of containers.
  • Step 3: Get the total volume.
Division for Unit Conversion
After finding the total volume in liters, you often need to convert it to another unit. For converting liters to kiloliters, we use division.
Remember the basic conversion factor:
- 1 kL = 1000 L
Now, if you have the total volume in liters, divide that number by 1000 to convert to kiloliters.
In our exercise, we have a total of 960 liters. To convert this to kiloliters:
\( 960 \text{ L} \times \frac{1 \text{ kL}}{1000 \text{ L}} = 0.96 \text{ kL} \)
This tells us that 960 liters is equal to 0.96 kiloliters.
  • Step 1: Find the total volume in liters.
  • Step 2: Use the conversion factor (divide by 1000) to get the volume in kiloliters.
  • Step 3: Express the solution in kiloliters.
Understanding this process helps in converting units effectively for various applications like chemistry, physics, and everyday activities.

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