Luas permukaan benda putar mengukur area yang terbentuk saat kurva diputar mengelilingi sumbu.
Rumus utama
Around x-axis: S = 2π integral y sqrt(1 + (dy/dx)2) dx
Around y-axis: S = 2π integral x sqrt(1 + (dx/dy)2) dy
Around y-axis: S = 2π integral x sqrt(1 + (dx/dy)2) dy
Contoh praktis
Sphere check: rotating a semicircle of radius r gives S = 4πr2.
Sumber terkait
Use Sphere, Cylinder, Cone, and cone/frustum guide.