A rectangular prism has a volume of 224 cubic centimeters . The
base of the box is 8 cm by 8 cm . What is the height of the box?

To find the height of the box, you can use the formula for the volume of a rectangular prism, which is given by:

Here, the base area can be calculated as length times width. Since the base is a square measuring 8 cm by 8 cm, the area is:

Now, you can set up the equation for volume:

To find the height, divide the volume by the base area:

Therefore, the height of the box is 3.5 cm.

Historical Background: Did you know that the concept of volume dates back to ancient civilizations? The Egyptians and Babylonians had methods to calculate the volume of various shapes including rectangular solids, which they used for trade and construction. Their ingenious techniques laid the foundation for modern geometry!

Real-World Application: Understanding volumes is crucial in various fields. For example, in architecture and construction, determining the correct volume is essential for ensuring that spaces are used effectively. Additionally, in the culinary world, chefs use volume measurements to accurately create recipes for everything, from baking to crafting sauces, ensuring consistent results!