what is the surface area of a sphere with a radius of 5 inches

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Let's find the surface area of a sphere with a radius of 5 inches. The formula for the surface area of a sphere is A equals 4 pi times r squared, where r is the radius. In our problem, the radius is 5 inches. Substituting this value into the formula, we get A equals 4 pi times 5 squared. 5 squared is 25, so we have A equals 4 pi times 25 square inches, which simplifies to 100 pi square inches. Therefore, the surface area of the sphere is 100 pi square inches. Let's visualize the surface area of a sphere with radius 5 inches. The surface of a sphere consists of infinitely many points, all equidistant from the center. This equidistance property is key to understanding the formula. Through calculus, mathematicians derived that the surface area equals 4 pi times the radius squared. For our sphere with radius 5 inches, we calculate 4 pi times 5 squared, which equals 4 pi times 25, giving us 100 pi square inches. This formula accounts for the entire surface of the sphere, as shown by the highlighted points on our visualization. Therefore, the surface area of the sphere is 100 pi square inches.