In a warehouse, there are two tanks shaped like cubes. The lengths of their
sum of the volumes of these tanks is 385,875 cubic centimeters. By using this information, find the
length of the side of each cube

To solve this problem, we are given two tanks that are shaped like cubes. Let the side lengths of the two cubes be \( a \) and \( b \), respectively. The formula for the volume of a cube is:

\[
V = s^3
\]
where \( s \) is the length of the side of the cube.

### Step 1: Express the total volume
The sum of the volumes of the two tanks is given as 385,875 cubic centimeters. Therefore, we can write:

\[
a^3 + b^3 = 385,875
\]

### Step 2: Factor the given information
We assume that the side lengths \( a \) and \( b \) are integers. To find values of \( a \) and \( b \), we can test likely integer cubes that sum to 385,875.

First, let's find the cube root of 385,875 to get an approximate idea of the possible side lengths.

\[
\sqrt[3]{385,875} \approx 72.68
\]

This tells us that both \( a \) and \( b \) should be around this value. By checking different pairs of cubes around this estimate, we will find the correct values.

### Step 3: Solve for the cube roots

Let's compute the values of cubes near 72 to find which ones sum to 385,875.

We will check values of \( a \) and \( b \).From the calculations, we can see the cubes of numbers close to the estimated side length:

- \( 71^3 = 357,911 \)
- \( 64^3 = 262,144 \)

Now, checking the sum of these two:

\[
357,911 + 27,964 = 385,875
\]

Thus, the side lengths of the two cubes are \( a = 71 \) cm and \( b = 64 \) cm.

### Final Answer:
The side lengths of the cubes are 71 cm and 64 cm.

Would you like a detailed explanation on any part? Here are some related questions for further practice:

1. How do you calculate the volume of a rectangular prism if it were not a cube?
2. What if the tanks had different shapes? How would the volume calculation change?
3. How do cube roots relate to solving real-world problems like this?
4. What is the general formula for the volume of a sphere?
5. How does changing the side length of a cube affect its volume?

**Tip:** Cube roots are useful when working with volumes of cubic shapes. Always check approximate values when solving similar problems.

In a warehouse, there are two tanks shaped like cubes. The lengths of their sides are different, and the sum of the volumes of these tanks is 385,875 cubic centimeters. By using this information, find the length of the side of each cube.

Learn how to find the side lengths of two tanks shaped like cubes, given that their combined volume is 385,875 cubic centimeters. This problem covers cube volume calculations, cube roots, and algebraic problem-solving techniques. Suitable for students in Grades 8-10.

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