r, or “radius: The radius is the distance from the center of the sphere to the edge of that sphere. π, or “pi:” This incredible number (equalling roughly 3. 14) represents the ratio between a circle’s circumference and diameter, and is useful in all equations with circles and spheres. It is commonly shortened as π = 3. 1416, but there are an infinite number of decimals. [3] X Research source 4: For somewhat complex reasons, the surface area of a sphere is always 4 times as large as the area of a circle with the same radius.
Advanced Tip:If you only know the volume of a sphere, you need to do a little more work to get the radius. Divide the volume by 4π, then multiply that answer by 3. Finally, take the cube root of this answer. [5] X Research source
If our radius is 5, like above, you would be left with 4 * 25 * π, or 100π.
100 * π = 100 * 3. 14 100π = 314
The full answer to the sphere in the pictures is: Surface Area = 314 units2. The units you use are always the same ones used to measure the radius. If the radius is in meters, the answer will be in meters. Advanced Tip: We square the units because area measures how many flat squares we could fit on the surface of the sphere. Say we measure the practice problem in inches. This means on a sphere where r=5, we could fit 314 squares on the surface of the sphere if the sides of every square are 1 inch long.
4πr2 r = 7 4 * π * 72 49 * 4 * π 196π Answer: Surface Area = 615. 75 centimeters2, or 615. 75 square centimeters.
Rotating a circle around its axis (the center point) will produce a sphere. Think of spinning a coin on the table and how it appears to form a sphere. While it won’t be explained here, this is where our equation comes from. Advanced Tip: Spheres have a smaller surface area per volume than any other shape – that means it can hold more things in a smaller area than any other shape.
