Step by step
The question
Question: find the volume of a cylinder with diameter 10 cm and height 3 cm.
1 Find the radius
The diameter goes all the way across the circle.
The radius is half of it.
Half of 10 is 10 divided by 2.
r = 102
10 divided by 2 is 5.
So r = 5 cm.
r = 5 cm
2 Circle times height
The top is a circle.
Its area is π × r².
The cylinder is that circle, stacked up 3 cm high.
π is a special number for circles.
It is about 3.14.
So the volume is V = π × r² × h.
V = π × r2 × h
Now put the numbers in: r = 5 and h = 3.
V = π × 52 × 3
5² means 5 times 5.
That is 25.
52 = 5 × 5 = 25
So V = π × 25 × 3.
V = π × 25 × 3
25 times 3 is 75.
So V = 75π.
We keep π in the answer.
That is the exact answer.
V = 75π cm3
3 About how much
To see about how much, put 3.14 for π.
V ≈ 75 × 3.14
75 times 3.14 is 235.5.
So the volume is about 235.5 cm³.
V ≈ 235.5 cm3
Let's look back.
First: find the radius.
Then: circle times height.
Last: about how much.
Answer
V ≈ 235.5 cm3