Step by step
The question
Question: what shape is the cut, if we slice a cylinder radius 3 parallel to the base, and what is its area?
cylinder radius 3, cut parallel to the base
A cross section is the flat face we see when we slice a solid.
cross section = the face of a cut
1 Look at the cut
Here is the cylinder.
We slice it parallel to the base.
The red face is the cut.
2 Name the shape
Flat, the cut looks like this.
The cut is the same as the round bottom: a circle.
So it is a circle.
= cut: a circle
Careful!
A cut parallel to the base always has the shape of the base.
Careful: parallel cut = the base shape
3 Find its area
A circle's area is π times the radius squared.
π times 9 is about 28.27.
= area = π × 3² ≈ 28.27
4 Check
Let's check: a cut parallel to the base has the shape of the base.
So the answer is right!
like the base: circle
Let's look back.
First: look at the cut.
Then: name the shape.
Then: find its area.
Last: check.
Answer
= area = π × 3² ≈ 28.27