Which is the formula for the surface area of a sphere with radius r?
S=4πr2
S=2/3πr3
S=4/3πr3
S=2πr2 ~~My choice
S=4πr2
http://www.google.com/#q=formula+for+the+surface+area+of+a+sphere+using+radius
The correct formula for the surface area of a sphere with radius r is S = 4πr^2. To understand how this formula is derived, we need to break it down.
A sphere is a perfectly symmetrical shape, meaning that all points on its surface are equidistant from its center. The surface area of a sphere is the total area covered by its curved surface.
To find the surface area of a sphere, we can imagine slicing it into infinitely many small pieces. Each piece can be approximated as a small circle with radius r, and the sum of the areas of all these small circles will give us the total surface area of the sphere.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Since each small circle represents a portion of the sphere's surface, we can sum up all these areas to find the total surface area of the sphere.
Since we are working with infinitely many small slices, we need to take the limit as the number of slices approaches infinity. This leads us to the integral form of the area formula. However, by knowing the result from mathematical proofs, we can skip the integral and directly use the derived formula for sphere surface area.
By summing up all the areas of the small circles, we find that the surface area of a sphere is given by S = 4πr^2. Therefore, your choice, S = 2πr^2, is incorrect.