GUIDE深度 · Deep dive
Volume and Surface Area Formulas
Volume is space occupied; surface area is the total outer area. Cuboid volume abc and surface 2(ab+ah+bh); cylinder volume πr²h and surface 2πr(r+h); sphere volume 4/3πr³ and surface 4πr².
Prisms/cylinders
Cuboid: abc, 2(ab+ah+bh).
Cylinder: πr²h, 2πr(r+h).
Curved solids
Sphere: 4/3πr³, 4πr².
Cone: 1/3πr²h.
Write the formula and unit first, then substitute values; check whether the solid is open or closed before using total surface area.
FAQ
Does surface area include bases?
Total surface includes them; subtract the opening for an open container.
Does a cone need slant height?
Not for volume; lateral area needs slant height.