How is volume calculated?

Volume is calculated using the formula that relates the area of the base of a three-dimensional object and its height. The formula is derived from the idea that volume represents the amount of space an object occupies. For most three-dimensional shapes, such as prisms or cylinders, the volume can be determined by multiplying the area of the base by the height of the object.

In this context, the area refers to the surface area of the base shape, and the height needs to be the perpendicular distance from the base to the top of the object. This approach allows you to extend the base area vertically to fill the three-dimensional space, effectively capturing the total volume of the shape. By using this method, it’s possible to calculate the volume for various geometric shapes, including cubes, rectangular prisms, and cylinders, thus making it a fundamental principle in geometry.

For example, if you have a rectangular prism with a base measuring 4 cm by 5 cm and a height of 10 cm, the area of the base is 20 cm². By multiplying this area by the height (10 cm), the total volume would be 200 cm³. This method validates why the correct answer focuses on the relationship between area and height in the calculation of