Subjects geometry

Sphere Area Volume 04F791

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1. **Problem statement:** We want to find the formulas for the surface area $O$ and volume $V$ of a sphere (kule). 2. **Surface area formula:** The surface area of a sphere with radius $r$ is given by the formula: $$O = 4\pi r^2$$ This formula comes from integrating the surface elements over the sphere. 3. **Volume formula:** The volume of a sphere with radius $r$ is given by: $$V = \frac{4}{3} \pi r^3$$ This formula is derived using calculus by integrating the volume of infinitesimal disks. 4. **Important notes:** - $\pi$ is a constant approximately equal to 3.14159. - $r$ is the radius of the sphere. - The formula $O = \pi r^2$ is the area of a circle, not the surface area of a sphere. - The formula $V = \frac{1}{3} G h$ is the volume of a cone or pyramid, not a sphere. 5. **Summary:** - Surface area of a sphere: $$O = 4\pi r^2$$ - Volume of a sphere: $$V = \frac{4}{3} \pi r^3$$