Solid of Revolution
y = sin(x), rotated about y-axis
Region: between y-axis
and x = arcsin(y),
from y = 0 to
y = 1
Disc radius: r(y) = arcsin(y)
Cross-section area: A(y) = π [arcsin(y)]²
V = π ∫₀¹ [arcsin(y)]² dy
= π(π²/4 − 2)
= π³/4 − 2π ≈ 1.4922
■Profile curve x = arcsin(y)
■Sample disc cross-sections
■Solid surface
Drag to rotate · Auto-rotating