Volume of a cone, step by step

A cone holds exactly a third of the cylinder it fits inside.

The question

A cone marked 3 cm, 2 cm tall

base × height

base:3.14 × 3 × 3 =28.26

base:28.26

28.26 × 2 =56.52

cylinder:56.52

3 cones fill 1 cylinder

56.52 ÷ 3 =18.84 cubic cm

Same idea as a box: the area of the base times how tall it is. Here the base is a circle, and that is the only difference.
The circle's area is π × r × r = 3.14 × 3 × 3 = 28.26 square cm.
Times the height: 28.26 × 2 = 56.52 cubic cm. That is the CYLINDER it fits inside, not the cone yet.
Now the part that gets forgotten. Exactly THREE cones fill the cylinder they sit inside — it is a fact about cones, not a number bolted onto a formula. So take a third: 56.52 ÷ 3 = 18.84 cubic cm.

How it works.

01
Same idea as a box: the area of the base times how tall it is. Here the base is a circle, and that is the only difference.
02
The circle's area is π × r × r = 3.14 × 3 × 3 = 28.26 square cm.
03
Times the height: 28.26 × 2 = 56.52 cubic cm. That is the CYLINDER it fits inside, not the cone yet.
04
Now the part that gets forgotten. Exactly THREE cones fill the cylinder they sit inside — it is a fact about cones, not a number bolted onto a formula. So take a third: 56.52 ÷ 3 = 18.84 cubic cm.