Surface Area and Volume – Formula Reference Sheet

Surface Area and Volume – Formula Reference Sheet

Surface Area and Volume -- Formula Reference Sheet

All the key formulas in one place. Bookmark this page for quick revision.

Table of contents

Notation
Cylinder
Regular square pyramid
Cone
Sphere
Complete summary table
Detailed articles

Notation

Symbol	Meaning
$r$	Radius of a circular base
$d$	Diameter ( $d = 2 r$ )
$h$	Height (perpendicular)
$s$	Slant height (cone)
$h_{s}$	Slant height (pyramid)
$a$	Base edge length (pyramid)
$π$	$\approx 3.14159$

Cylinder

Quantity	Formula
Base area	$S_{base} = π r^{2}$
Lateral area	$S_{lateral} = 2 π r h$
Total surface area	$S = 2 π r (r + h)$
Volume	$V = π r^{2} h$

Full article: Cylinder

Regular square pyramid

Quantity	Formula
Slant height	$h_{s} = h^{2} + (a /2)^{2}$
Base area	$S_{base} = a^{2}$
Lateral area	$S_{lateral} = 2 a \cdot h_{s}$
Total surface area	$S = a^{2} + 2 a \cdot h_{s}$
Volume	$V = \frac{1}{3} a^{2} h$

Full article: Pyramid

Cone

Quantity	Formula
Slant height	$s = r^{2} + h^{2}$
Base area	$S_{base} = π r^{2}$
Lateral area	$S_{lateral} = π r s$
Total surface area	$S = π r (r + s)$
Volume	$V = \frac{1}{3} π r^{2} h$

Full article: Cone

Sphere

Quantity	Formula
Surface area	$S = 4 π r^{2}$
Volume	$V = \frac{4}{3} π r^{3}$

Full article: Sphere

Complete summary table

Solid	Surface area	Volume
Cylinder	$2 π r (r + h)$	$π r^{2} h$
Pyramid	$a^{2} + 2 a \cdot h_{s}$	$\frac{1}{3} a^{2} h$
Cone	$π r (r + s)$	$\frac{1}{3} π r^{2} h$
Sphere	$4 π r^{2}$	$\frac{4}{3} π r^{3}$

Pattern to remember: Solids that taper to a point (pyramid, cone) have $\frac{1}{3}$ in the volume formula. The sphere is special with $\frac{4}{3}$ .

Detailed articles