Volume Formulas for 3D Shapes

Direct answer

What is a volume formula?

Volume formulas calculate the space inside a 3D solid. Common examples are cube volume $V = s^{3}$ , rectangular prism volume $V = l w h$ , cylinder volume $V = π r^{2} h$ , cone volume $V = \frac{1}{3} π r^{2} h$ , and sphere volume $V = \frac{4}{3} π r^{3}$ .

Quick table

Volume formulas table

Shape	Formula	Use
Cube	$V = s^{3}$	s = side length
Rectangular prism	$V = l w h$	l = length, w = width, h = height
Cylinder	$V = π r^{2} h$	r = radius, h = height
Cone	$V = \frac{1}{3} π r^{2} h$	r = radius, h = height
Sphere	$V = \frac{4}{3} π r^{3}$	r = radius
Pyramid	$V = 1/3 B h$	B = base area, h = height

Formula cards

Quick formula cards

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Circle Formulas

Area $A = π r^{2}$

Circumference $C = 2 π r = π d$

Diameter $d = 2 r$

Radius $r = \frac{d}{2}$

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Triangle Formulas

Area $A = \frac{1}{2} bh$

Perimeter $P = a + b + c$

Right triangle $a^{2} + b^{2} = c^{2}$

Heron's formula $A = s (s - a) (s - b) (s - c)$

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Cylinder Formulas

Volume $V = π r^{2} h$

Lateral surface area $L S A = 2 π r h$

Total surface area $T S A = 2 π r (r + h)$

Base area $B = π r^{2}$

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Cone Formulas

Volume $V = \frac{1}{3} π r^{2} h$

Lateral surface area $L S A = π r l$

Total surface area $T S A = π r (r + l)$

Slant height $l = r^{2} + h^{2}$

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Sphere Formulas

Volume $V = \frac{4}{3} π r^{3}$

Surface area $S A = 4 π r^{2}$

Diameter $d = 2 r$

Radius $r = \frac{d}{2}$

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Examples

Step-by-step examples

Rectangular prism volume

Given l = 8 cm, w = 4 cm, h = 3 cm.
Use $V = l w h$ .
$V = 8 \times 4 \times 3 = 96 c m^{3}$ .

Cylinder volume

Given r = 2 m and h = 9 m.
Use $V = π r^{2} h$ .
$V = 36 π \approx 113.10 m^{3}$ .

Sphere volume

Given r = 5 in.
Use $V = \frac{4}{3} π r^{3}$ .
$V = 500/3 π \approx 523.60 i n^{3}$ .

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FAQ

Volume Formulas FAQ

What is the easiest volume formula?

For prisms, volume is usually base area times height, or $V = B h$ .

Why does a cone use one third?

A cone with the same base and height as a cylinder has one third of the cylinder volume.

Do volume answers need cubic units?

Yes. Volume is written in cubic units, such as cm3 or cubic meters.