Surface Area

Surface area is a measure of the total area that the surface of a three-dimensional object occupies. It is crucial for understanding the properties of solids in various applications, including real-world problems.

Formula Overview

The surface area formulas for some common shapes are as follows:

• Cube: $SA = 6s^{2}$, where $s$ is the length of a side.
• Rectangular Prism: $SA = 2lw + 2lh + 2wh$, where , , and are the length, width, and height respectively.

Worked Example

Find the surface area of a cylinder with a radius of 3 units and a height of 5 units.

1. Identify the radius and height: $r = 3$, $h = 5$.
2. Use the formula for the surface area of a cylinder: $SA = 2\pi r(h + r)$.

Key Questions

• What is the surface area of a cube with a side length of 4 units?
• How do you calculate the surface area of a rectangular prism with dimensions 2, 3, and 4 units?
• If a sphere has a radius of 5 units, what is its surface area?
• How does the height of a cylinder affect its surface area?
• Can the surface area be negative? Why or why not?

Keywords

• Surface Area
• Cylinder
• Sphere
• Cube
• Rectangular Prism