How to find the total surface area of a sphere?
Understand the Problem
The question is asking for the formula or method to calculate the total surface area of a sphere. This involves understanding the geometric properties of a sphere and the mathematical formula used to find its surface area.
Answer
$ A = 4 \pi r^2$
Answer for screen readers
The formula to find the total surface area of a sphere is $ A = 4 \pi r^2$
Steps to Solve
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Identify the radius of the sphere
The radius $r$ is the distance from the center of the sphere to any point on its surface.
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Use the surface area formula for a sphere
The surface area $A$ of a sphere is given by the formula: $$ A = 4 \pi r^2 $$
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Calculate the surface area
Substitute the radius $r$ into the formula to find the surface area.
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Example calculation
Suppose the radius of the sphere is 5 units. Plugging this into the formula, we get: $$ A = 4 \pi (5)^2 = 4 \pi \times 25 = 100 \pi $$ Therefore, the surface area is $100 \pi$ square units.
The formula to find the total surface area of a sphere is $ A = 4 \pi r^2$
More Information
The total surface area of a sphere can be derived from a more general formula for the surface area of an ellipsoid. Also, it’s interesting to know that Archimedes was the first to derive this formula.
Tips
A common mistake is to confuse the surface area formula with the volume formula of a sphere, which is $ V = \frac{4}{3} \pi r^3 $. Always check which formula is required.
