why surface area of sphere is not equal to 2 * pi^2 * r^2 ?

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Pretty much the title, Cannot fathom why titled formula is invalid or not in use?
We take half the vertical cirucmference, pi * r and rotate it around the horizontal periphery on its axis, 2 * pi * r, this should give the value of surface area.

Pic just for reference –
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In: Mathematics

3 Answers

Anonymous 0 Comments

Let’s imagine a point on that vertical half-circumference. First, let’s imagine the point is on the equator. When we rotate it around the vertical axis, it does indeed travel the circumference 2*pi*r. But what if we imagine the point is close to the pole? When we rotate it around the vertical axis, it travels in a much smaller circle, much less than 2*pi*r. So, that part contributes much less to the total surface area. Your formula works only if the horizontal distance from the vertical axis to the surface is the same everywhere, which is true for a cylinder, not a sphere.

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