Find total outer area of standard solids for paint, material, and geometry problems.
Overview
Surface area measures the total area covering a 3D object’s exterior. Paint, wrapping paper, and heat transfer estimates depend on correct solid formulas, not volume alone.
Each shape has a dedicated equation: sphere 4πr², cylinder 2πr²+2πrh including caps if closed, cube 6s². Composite solids require summing visible faces minus hidden glued interfaces.
Units square when measuring area: m², ft². Do not mix radius with diameter in formulas; halving diameter errors sphere area by a factor of four.
In applied problems, add waste margin for material sheets and account for openings (doors, windows) subtracted from total coated area in architectural estimates.
Steps
Choose sphere, cylinder, cube, cone, etc.
Radius, height, side length with consistent units.
Include end caps on cylinders when closed.
Apply solid-specific surface area formula.
Add areas of combined simple solids.
Square linear units for area output.
Math
Sphere: A = 4πr²; Cylinder (closed): A = 2πr² + 2πrh
Surface area sums areas of all external faces or curved surfaces of the solid.
Worked cases
A = 4π×25 = 100π
≈ 314.16 square units.
6×4² = 96
96 square units.
Lateral 2πrh plus one base if open top only
Depends on included faces; specify caps.
Why use this
Questions