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Calculate volume, lateral surface area, total surface area, and slant height of a right circular cone.
A cone is a 3D shape with a circular base that tapers to a single point called the apex. The formulas here apply to right circular cones where the apex is directly above the center of the base.
This factor comes from calculus (integration). Imagine stacking infinitely thin circular disks from base to apex - each disk gets smaller, and the total volume is ⅓ of the enclosing cylinder.
The curved surface has arc length = circumference = 2πr at the base. When unrolled, the radius of the sector is the slant height l. The sector angle is (r/l) × 360°.
An oblique cone has its apex not directly above the base center. The volume formula still works, but surface area calculations become more complex.
Ice cream cones, traffic cones, party hats, funnels, volcanic mountains (approximately), and many architectural roofs use cone shapes.
A cone is like a pyramid with infinitely many sides (circular base). Both use V = ⅓ × Base × Height. As a pyramid's base gains more sides, it approaches a cone.