Fish Tank Volume: Solving Roberto's Water Problem

Hey guys! Let's dive into a fun math problem involving Roberto's fish tank. We're going to figure out the volume of water it holds when only partially filled. This is a classic example of a volume calculation, perfect for anyone looking to brush up on their math skills or just curious about how much water goes into a tank. So, grab your calculators (or your thinking caps) and let's get started! Understanding volume is super important in all sorts of real-world scenarios, from figuring out how much liquid a container can hold to calculating the space occupied by a 3D object. In this case, we're applying that knowledge to Roberto's fish tank. Remember, volume is the amount of space an object occupies, often measured in cubic units like inches cubed (in³), as in our case. The problem gives us a few key pieces of information: the total volume of the fish tank and the percentage to which it's filled with water. We will use the original problem to explain step by step and break down the problem-solving process. The original problem is: If the volume of Roberto’s fish tank is 4,320 inches³ and he only fills it with 75% of water, what is the volume of the water in the fish tank?

First, we need to understand what the problem is asking. We are given the total volume of the fish tank and the percentage of that volume that is filled with water. The goal is to calculate the actual volume of the water within the tank. The total volume of the tank is 4,320 cubic inches. This is the maximum amount of space the tank can hold. However, Roberto doesn't fill the tank completely. He fills it to 75% of its capacity. This means that only a portion of the total volume is occupied by water. To solve this, we will first convert the percentage to a decimal, then multiply the total volume of the tank by the decimal to find the volume of the water. This method provides a clear and straightforward path to the solution. The core concept here is proportional reasoning. We are essentially finding a fraction of the total volume. It's like saying, if the whole tank represents 100%, and we only fill it to 75%, then the water volume is 75% of the total tank volume. The steps required are simple arithmetic operations, making the problem accessible. Let's move onto the step-by-step solution.

Step-by-Step Solution

Alright, let's break down the problem of finding the water volume in Roberto's fish tank step by step. This method makes it easier to follow and understand the calculations. We will take the given information, apply the correct formulas, and arrive at the solution. Here's a detailed, easy-to-follow guide:

Step 1: Convert Percentage to Decimal

The first thing we need to do is convert the percentage into a decimal. Percentages are just a way of expressing a fraction of 100. To convert 75% to a decimal, you divide it by 100. So, 75% becomes 75 / 100 = 0.75. This decimal represents the fraction of the tank that is filled with water. It's like saying the tank is 0.75 full. Converting percentages to decimals is a fundamental skill in math and is super useful in all kinds of calculations. This step is crucial because it allows us to perform mathematical operations easily. Without converting, we would not be able to accurately calculate the water volume. Make sure you don't skip this step! It is a key element of the problem-solving process. Remember this conversion: percentage / 100 = decimal. In our case, 75% / 100 = 0.75.

Step 2: Calculate the Volume of Water

Now, we know the total volume of the fish tank (4,320 in³) and the fraction that is filled with water (0.75). To find the volume of the water, we multiply these two values. So, we do the following calculation: 4,320 in³ * 0.75 = 3,240 in³. This means that the volume of the water in Roberto's fish tank is 3,240 cubic inches. This is the answer to our problem! The multiplication step combines the total capacity of the tank with the fraction that is water, to give us the actual volume of the water. It's a direct application of the concept of finding a percentage of a quantity. When you calculate, always remember to include the units. In this case, our unit is cubic inches (in³). This is important because it shows what we are measuring—the space that the water occupies.

Conclusion

There you have it, guys! We have successfully calculated the volume of water in Roberto's fish tank. By following a step-by-step approach, we converted the percentage to a decimal and multiplied it by the total volume of the tank. The volume of the water in the tank is 3,240 cubic inches. This problem demonstrates a practical application of volume calculation and percentage conversion. It shows how these concepts are used in everyday situations, from filling a fish tank to understanding the capacity of containers. Now you know how to solve a volume problem! Remember, practice is key to mastering these types of problems. So, try similar problems and apply these steps to enhance your skills. Volume calculations come up frequently in many fields, like engineering, architecture, and even in cooking or gardening when measuring liquids or solids. Knowing how to convert percentages and perform these simple volume calculations can be super helpful in a lot of situations. Hopefully, this explanation was clear and easy to follow. Remember the main steps: convert the percentage to a decimal, multiply the tank’s total volume by the decimal. Keep practicing, and you'll become a pro at these problems in no time. If you have any questions, feel free to ask! Understanding the volume of water in the tank helps with figuring out other things, like how much fish food to use or how many fish to put in the tank. Awesome job, and keep up the great work!