## Surface Area of a Sphere

### The surface area of a sphere is the total area of the curved surface that covers the sphere

The surface area of a sphere is the total area of the curved surface that covers the sphere. To calculate the surface area, you can use the formula:

Surface Area = 4πr²

Where:

– Surface Area is the total area of the sphere’s surface

– π (pi) is a mathematical constant approximately equal to 3.14159

– r is the radius of the sphere (the distance from the center of the sphere to any point on its surface)

To understand why this formula works, let’s break it down. Imagine cutting a sphere into a series of tiny flat pieces, called infinitesimal elements. Each element is approximately like a little disk, and when you add up all these elements, you get the total surface area of the sphere.

Each infinitesimal element has an area proportional to the radius squared (r²) and the circular shape of the element. The constant 4π comes from the proportions of the complete sphere and relates how many disks can fit along the curved surface.

By summing up all these infinitesimal elements, we obtain the surface area of the entire sphere.

So, when you have the radius of a sphere, you can use the formula Surface Area = 4πr² to find the total surface area.

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