Surface Area and Volume

Surface Area & Volume

The surface area of a 3D figure or object is the total area of the figure's surface. Though our formulas we use condense the calculations with multiplication, we are simply finding the area of each side of the figure and adding it together for a total area.

When calculating area of 2D objects, area was always in square units. This is the case for surface area as well, even if we are dealing with a 3D object. This makes sense because for surface area, we are finding the area of 2D faces of a figure and then adding them together; the area calculations remain the same.

A good way to visualize this is to imagine a box. When you flatten the box completely, it is essentially a 2D shape. The area of all of the different connected sections of flattened box is the surface area of the box.

The volume of a figure, on the other hand, is the quantity of 3D space enclosed by a figure. In real life, we often measure volume in L or mL. As an example, the volume of a can of soda is typically 355 mL.

Unlike area or surface area, volume is measured in cubic units. Instead of cm² or m², surface area is measured in cm³ or m³. And though mL (milliliters) or L (liters) do not look like cubic units, 1 mL is actually equal to 1 cm³. We usually use mL to talk about liquids, but cm³ can also be used as well - it is just less common in real life.

Though volume and area are totally different, we see that our volume formulas contain calculations for area. In the section below, I go into why we see these "area components" in volume calculations. Of course, you can just memorize the formulas or use a formula sheet - so this content is entirely optional for working with volume - but I promise you that having an intuitive understanding of the formulas will improve your problem solving abilities with geometry problems.

Volume: Visualizing the Formulas

In the video below, I go over a few of the formulas we will use for calculating volume and provide a visual understanding of how the formulas work (no crazy math, I promise).

General Formulas

Solving Problems Involving Surface Area & Volume