Finally, we turn to the kinds of shapes we see in our daily lives: 3D shapes. Now, by contrast to 2D shapes, 3D shapes appear on relatively few GRE problems, so it may help your scores more to really master the different aspects of 2D shapes.
There are two main 3D shapes that the GRE tests on: the "rectangular solid" (also known as the rectangular prism) and the cylinder (also called the "right circular cylinder").
And there are two main properties of such objects that we will care about:
- Surface Area: this is the total area of all the surfaces of a 3D shape
So, in a rectangular solid, we add up the area of each of the 6 sides. And, in a cylinder, we add up the area of the circle on the top, the circle on the bottom, and the curved portion in between the two.
- Volume: the space enclosed by a 3D shape
Imagine filling up the 3D shape with water. The amount of space that the water takes up, that’s the volume of the object.
By analogy, you could think of the area of a 2D shape as capturing how much space the lines enclosed. Similarly, volume is a measure of how much space the surfaces of a 3D shape enclose.
In subsequent posts, we will talk about the rectangular solid and cylinder in greater detail and show how to calculate the surface area and volume for each.