Step by step
The question
Question: find the surface area of a cone with diameter 10 and slant height 8.
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.
10 divided by 2 is 5.
So r = 5.
2 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.
3 The base
The base is a circle with radius 5.
A circle is π × r².
Now put the numbers in: r = 5.
5² means 5 times 5.
That is 25.
So the base is 25π.
4 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 = 5 and l = 8.
5 times 8 is 40.
So the side is 40π.
5 Add the parts
Now we add the base and the curved side.
25 plus 40 is 65.
So S = 65π.
We keep π in the answer.
That is the exact answer.
6 About how much
To see about how much, put 3.14 for π.
65 times 3.14 is 204.1.
So the surface area is about 204.1 square units.
Let's look back.
First: find the radius.
Then: count the parts.
Then: the base.
Then: the curved side.
Then: add the parts.
Last: about how much.