Milk Carton Volume: Will It Hold A Liter?
Hey guys! Ever wondered if that milk carton really holds a full liter? We're diving into a cool math problem today that tackles this exact question. A certain brand of milk comes in a paralelepiped carton (fancy word for a box!), and we need to figure out if it can actually hold a liter of milk. Let's get started!
Decoding the Milk Carton: Dimensions and Volume
First, let's break down the specifics. This milk carton, our paralelepiped friend, has the following dimensions:
- Width: 11 cm
- Height: 15 cm
- Depth: 6 cm
Now, to figure out how much milk this carton can hold, we need to calculate its volume. Remember back to your geometry days? The volume of a paralelepiped (or a rectangular prism, which is the same thing) is found by multiplying its length, width, and height. In our case, that's width x height x depth. So, let’s plug in those numbers:
Volume = 11 cm * 15 cm * 6 cm
Calculating this, we get a volume of 990 cubic centimeters (cm³). But what does that even mean in terms of liters? This is where the conversion factor comes in handy. We need to know how cubic centimeters relate to liters to determine if the carton can hold a full liter of milk.
Cubic Centimeters to Liters: Making the Conversion
Here's the key piece of information: 1 liter is equal to 1000 cubic centimeters (1 L = 1000 cm³). This is a crucial conversion factor that links volume in cubic centimeters, which we calculated, to volume in liters, which is what we're trying to compare to.
Now that we know this, we can easily see if our milk carton holds a liter. We calculated the volume to be 990 cm³, and a liter is 1000 cm³. So, we're almost there, but not quite!
The Verdict: Does It Hold a Liter?
Okay, guys, time for the big reveal! We found that the milk carton has a volume of 990 cm³. We also know that 1 liter is equal to 1000 cm³. Comparing these two values, we can see that the carton's volume (990 cm³) is slightly less than a liter (1000 cm³).
So, the answer is: No, the milk carton does not have enough space to hold a full liter of milk. It's just a little bit short. This might seem surprising, but it's a good reminder that even though something looks like it should hold a certain amount, it's always best to do the math and check! This is a practical example of how understanding volume and unit conversions can be useful in everyday life. Imagine buying several of these cartons thinking you're getting a liter each, and you'd actually be slightly short on your total milk purchase! It also highlights the importance of accurate labeling and packaging in the food and beverage industry.
Why Does This Matter? The Importance of Accurate Measurements
You might be thinking,
