By Karl Wallulis Updated Aug 30, 2022
Three‑dimensional solids—such as spheres, cylinders, and rectangular prisms—are described by two fundamental metrics: volume and surface area. Volume quantifies the space the solid occupies (measured in cubic units), while surface area sums the flat areas of all exposed faces (measured in square units).
A rectangular prism is a box‑shaped solid whose cross‑sections are always rectangles. Common examples include LEGO bricks and Rubik’s cubes.
Volume: V = l × w × h (where l = length, w = width, h = height)
Surface area: SA = 2(lw + wh + lh)
A sphere is the 3‑D analogue of a circle: every point on its surface is the same distance (radius r) from its center.
Volume: V = (4/3)πr3
Surface area: SA = 4πr2
A cylinder consists of two parallel, congruent circular bases connected by a curved surface. A soda can is a familiar example.
Volume: V = πr2h
Surface area: SA = 2πr2 + 2πrh (lateral area + two bases)
A cone is formed by tapering a cylinder’s sides to a single apex.
Volume: V = (1/3)πr2h
Surface area: SA = πr2 + πrs (base + lateral area), where s is the slant height.
