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### The expression 4πr^2 represents the formula for the surface area of a sphere

The expression 4πr^2 represents the formula for the surface area of a sphere. In this formula, “r” refers to the radius of the sphere, and “π” (pi) represents the mathematical constant approximately equal to 3.14159.

To understand how the formula is derived, let’s break it down step by step:

1. The formula starts with “r^2”, which means raising the radius to the power of 2. This is done to calculate the area of the circular base of the sphere. The base area is found by multiplying the square of the radius by π.

2. The next step is multiplying the base area by 4. This is because a sphere is a three-dimensional shape, and it consists of two identical hemispheres. So, by multiplying the base area of one hemisphere by 2, we get the total area of the sphere. Further, by multiplying it by 2 again, we account for both the top and bottom hemispheres.

3. Finally, the constant π (pi) is included to ensure accurate calculations. Pi is an irrational number that represents the ratio of the circumference of a circle to its diameter.

By using the formula 4πr^2, you can find the surface area of any sphere by plugging in the appropriate value for the radius.

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