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Why is the volume of sphere [math]\frac43 \pi r^3[/math]?
Can you explain to me why the volume of a sphere is [math]\frac43 \pi r^3[/math]?
Sure! The formula for the volume of a sphere is derived by integration. Imagine slicing the sphere into infinitely thin disks, each with thickness dx. The volume of a single disk can be approximated as the area of the disk multiplied by its thickness, which is [math]\pi r^2 dx[/math]. By summing up all of these disks from 0 to the radius of the sphere, we arrive at the formula [math]\frac43 \pi r^3[/math].