Volumes by Integration

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Hook

Spin a curve into a solid

Spin a curve around an axis and it carves out a solid — a bowl, a cone, a sphere. To find its volume, slice it into infinitely thin disks and sum their volumes. The disk method turns rotation into an integral — calculus sculpting in 3D.

Disk: V = π∫[radius]² dx. Washer: subtract the hole.