Step by step
The question
Question: find the volume of a cone with radius 6 and height 7.
1 A third of the cylinder
Draw a cylinder around the cone, with the same base and the same height.
Fill the cone with water 3 times.
That fills the cylinder exactly.
So the cone is one third of the cylinder.
π is a special number for circles.
It is about 3.14.
The cylinder is π × r² × h.
So the cone is V = ⅓ × π × r² × h.
Now put the numbers in: r = 6 and h = 7.
6² means 6 times 6.
That is 36.
So V = ⅓ × π × 36 × 7.
Keep the numbers small: divide 36 by 3 first.
36 divided by 3 is 12.
So V = π × 12 × 7.
12 times 7 is 84.
So V = 84π.
We keep π in the answer.
That is the exact answer.
2 About how much
To see about how much, put 3.14 for π.
84 times 3.14 is 263.76.
So the volume is about 263.76 cubic units.
Let's look back.
First: a third of the cylinder.
Last: about how much.