Formula

Volume of a right circular cone

Mensuration • Solids • Cone

Formula

V = \frac{1}{3} π r^{2} h

A right circular cone of base radius

r

and vertical height

h

has volume

\frac{1}{3} π r^{2} h

, which is one third of the cylinder standing on the same base with the same height.

How to use it

1Use the vertical height, not the slant height; where only the slant height $l$ is given, recover $h = l^{2} - r^{2}$ first.
2To count how many containers of given capacity a conical vessel fills, divide its volume by that capacity.
3Cancel the $7$ of $π = \frac{22}{7}$ against the radius before multiplying, to keep the decimals short.

A conical vessel has base radius

7

cm and vertical height

9

cm. Find its capacity.

Step-by-step

1
$V = \frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 9$
Why: The height used is the vertical one, measured from base to apex.
2
$= \frac{1}{3} \times 22 \times 7 \times 9 = 462$ cm $^{3}$

Answer

462

^{3}

Watch out

Dropping the

\frac{1}{3}

triples the answer, and substituting the slant height for the vertical height overstates it; option lists routinely print both of those values.

Builds on

Also known as

volume of a cone, one third pi r squared h, capacity of a conical vessel