Step by step
The question
Question: find the volume of a cone with radius 6 and height 10.
There are four choices.
First we solve it, the normal way.
Then we pick.
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: the way round is about 3.14 times the way across.
The cylinder is circle area times height: π × r² × h.
So the cone is V = ⅓ × π × r² × h.
Now put the numbers in: r = 6 and h = 10.
6² means 6 times 6.
That is 36.
So V = ⅓ × π × 36 × 10.
⅓ of 36 means 36 divided by 3.
We can multiply in any order.
So we do that first: it keeps the numbers small.
36 divided by 3 is 12.
So ⅓ × 36 becomes 12.
So V = π × 12 × 10.
12 times 10 is 120.
So V = 120π.
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.
120 times 3.14 is 376.8.
So the volume is about 376.8 cubic units.
3 Pick the choice
Our answer is V ≈ 376.8.
That is choice B.
4 Why not the others
A is 62.8.
Wrong: forgot to square the radius.
C is 1130.4.
Wrong: forgot the 1/3: that is a cylinder.
D is 1507.2.
Wrong: used the diameter 12 instead of the radius.
Let's look back.
First: a third of the cylinder.
Then: about how much.
Then: pick the choice.
Last: why not the others.