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Calculate volume, curved surface area, and total surface area of a hemisphere (half of a sphere).
A hemisphere is exactly half of a sphere, created by cutting a sphere with a plane through its center. The flat circular face is called the base.
Hemispheres appear in dome architecture, bowls, headlights, radar domes (radomes), igloos, stadium roofs, and astronomical observatories. The geodesic dome is based on a hemisphere.
Curved surface area (2πr²) is just the dome part. Total surface area (3πr²) includes the flat circular base. Use curved when the base is open, total when it's solid.
A full sphere has volume (4/3)πr³. Since a hemisphere is exactly half, its volume is (4/3)πr³ ÷ 2 = (2/3)πr³.
Both have circular bases. A cone with same base and height as a hemisphere has volume (1/3)πr³, which is half the hemisphere's volume. The hemisphere is "fuller".
Domes (Capitol building, planetariums), salad bowls, igloos, some helmets, contact lenses (roughly), and the Earth divided at the equator into Northern and Southern hemispheres.
The curved shape distributes forces evenly, allowing domes to span large areas without internal supports. Forces flow through the curve to the base, similar to how arches work.
From V = (2/3)πr³, solve for r: r = ∛(3V/(2π)). For example, if V = 100, r = ∛(150/π) ≈ 3.63.