Cambridge IGCSE Mathematics · Syllabus 0580 · Mensuration
Surface Area and Volume
What is Surface Area and Volume?
Volume is the amount of space a solid occupies, measured in cubed units, and surface area is the total area of the faces enclosing it, measured in squared units. A cuboid has volume lwh and surface area 2(lw + lh + wh). A prism is any solid with a uniform cross-section, so its volume is the cross-sectional area multiplied by its length and its surface area is two cross-sectional ends plus the lateral faces formed along the cross-section perimeter. A cylinder has volume pi r squared h and curved surface area 2 pi r h, with 2 pi r squared more for the two ends. A pyramid has volume one third of the base area times the perpendicular height, and its surface area is the base plus its triangular faces. A cone has volume one third pi r squared h and curved surface area pi r l, where l is the slant height and, for a right cone, l squared equals r squared plus h squared. A sphere has volume four thirds pi r cubed and surface area 4 pi r squared, and a hemisphere has half that volume, a curved surface of 2 pi r squared and a total surface of 3 pi r squared when its flat circular face is exposed.
This definition is part of the Mensuration chapter in Cambridge IGCSE Mathematics.