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Find the surface area of the given sphere to the nearest tenth.

Firstly, we recall the formula we need for finding the surface area of a sphere. It’s four 𝜋𝑟 squared, where 𝑟 represents the sphere’s radius. That’s the distance between the center of the sphere and any point on the sphere’s surface. From the figure, we can see that the radius of this sphere is six centimeters. So we can substitute this value of 𝑟 directly into our formula, giving four 𝜋 multiplied by six squared. And we must remember that it is only the radius that we need to square. Now, we can simplify six squared is 36 and four multiplied by 36 is 144. So the exact surface area of this sphere is 144𝜋.

However, the question asks us to give this answer to the nearest tenth. So we can use a calculator to evaluate this as a decimal. And it gives 452.3893. If we’re rounding to the nearest tenth, then our deciding digit is the eight in the hundredths column which tells us that we need to round up. So we have a value of 452.4. As the units for the radius were centimeters, the units for the surface area of the sphere will be square centimeters. So we have our answer to the problem. The surface area of this sphere to the nearest tenth is 452.4 square centimeters.

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