Step by step
The question
Question: find the surface area of a cone with radius 4 cm and slant height 6 cm.
1 Count the parts
The surface area is the area of all the outside.
A cone has a circle at the bottom and a curved side.
2 The base
The base is a circle with radius 4 cm.
A circle is π × r².
Now put the numbers in: r = 4.
4² means 4 times 4.
That is 16.
So the base is 16π.
3 The curved side
Cut the curved side open and lay it flat.
It is part of a bigger circle.
Its area is π × r × l.
Careful: l is the slant height, down the side.
Not the height inside the cone.
π is a special number for circles.
It is about 3.14.
So the curved side is π × r × l.
Now put the numbers in: r = 4 and l = 6.
4 times 6 is 24.
So the side is 24π.
4 Add the parts
Now we add the base and the curved side.
16 plus 24 is 40.
So S = 40π.
We keep π in the answer.
That is the exact answer.
5 About how much
To see about how much, put 3.14 for π.
40 times 3.14 is 125.6.
So the surface area is about 125.6 cm².
Let's look back.
First: count the parts.
Then: the base.
Then: the curved side.
Then: add the parts.
Last: about how much.