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Calculate volume and surface area of a spherical cap (dome). Enter sphere radius R and cap height h.
A spherical cap is the portion of a sphere cut off by a plane. It's like slicing a ball with a knife - the smaller piece is the cap, and the larger piece is the "segment."
Domes, igloos, observatory roofs, contact lens shapes, helmet crowns, bowl bottoms, and the visible portion of partially submerged spheres.
Archimedes proved that the curved surface area of a spherical cap equals the area of a cylinder with radius R and height h. This is known as Archimedes' hat-box theorem.
From a² = h(2R - h), you can solve the quadratic: h = R - √(R² - a²). This gives the smaller cap; the larger cap has h = R + √(R² - a²).
A cap is cut by one plane (has one flat base), while a segment is cut by two parallel planes (has two flat bases, like a slice of orange).