Welcome! Today we'll learn how to calculate the surface area of a sphere. A sphere is a perfectly round three-dimensional object where every point on its surface is exactly the same distance from the center. This distance is called the radius.
The formula for the surface area of a sphere is A equals 4 pi r squared. This means we multiply 4 times pi times the radius squared. Notice that this is exactly 4 times the area of a circle with the same radius. A circle has area pi r squared, while a sphere has surface area 4 pi r squared.
Let's work through an example. Suppose we have a sphere with radius 3 units. We start with our formula A equals 4 pi r squared. We substitute r equals 3, giving us A equals 4 pi times 3 squared. This becomes 4 pi times 9, which equals 36 pi. Using the approximation pi equals 3.14159, we get approximately 113.1 square units.
To summarize, the surface area of a sphere is given by the formula A equals 4 pi r squared. This is exactly 4 times the area of a circle with the same radius. To solve problems, simply substitute the radius value and calculate. Always remember to include proper units in your final answer. This important formula appears frequently in physics, engineering, and geometry applications.
The formula for the surface area of a sphere is A equals 4 pi r squared. This means we multiply 4 times pi times the radius squared. Notice that this is exactly 4 times the area of a circle with the same radius. A circle has area pi r squared, while a sphere has surface area 4 pi r squared.
Let's work through an example. Suppose we have a sphere with radius 3 units. We start with our formula A equals 4 pi r squared. We substitute r equals 3, giving us A equals 4 pi times 3 squared. This becomes 4 pi times 9, which equals 36 pi. Using the approximation pi equals 3.14159, we get approximately 113.1 square units.