Write a word problem whose solution involves taking a cube root. State the problem and solve it, showing and explaining all steps.

I take it you're looking for an idea - you could write a problem about a cube-shaped object, such as a die.

A cube has a volume of 100 cm^3

How long is each of its sides ?

x^3 = 100
take the cube root of 100, use your calculator

Problem:

A farmer has a field that measures 216 cubic meters. He wants to determine the length of one side of the field, assuming it is in the shape of a perfect cube. What is the length of one side of the field?

Solution:
To solve this problem, we need to find the cube root of the volume of the field (216 cubic meters).

Step 1: Cube Root Calculation
To find the cube root, we can use a scientific calculator or a math software, which usually has a cube root function. In this case, the cube root of 216 is equal to 6.

Step 2: Interpretation
Therefore, the length of one side of the farmer's field is 6 meters.

Explanation:
The cube root is the inverse operation of cubing a number. By taking the cube root of a number, we find the value that was cubed to produce that number.

In this problem, we are given the volume of a field, which represents the total amount of space it occupies. We assume that the field is in the shape of a perfect cube, which means all sides have the same length.

To find the length of one side, we need to find the cube root of the volume. In this case, the cube root of 216 is 6, which means that 6 cubed (6^3) equals 216. Therefore, the length of one side of the field is 6 meters.

Note: If the volume of the field were different, the cube root would yield a different result.

Write a word problem whose solution is -70=70.