Surface area of cone radius 3 slant height 5

Step by step

The question

Question: find the surface area of a cone with radius 3 and slant height 5.

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 3.

A circle is π × r².

Now put the numbers in: r = 3.

3² means 3 times 3.

That is 9.

So the base is 9π.

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 = 3 and l = 5.

3 times 5 is 15.

So the side is 15π.

4 Add the parts

Now we add the base and the curved side.

9 plus 15 is 24.

So S = 24π.

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.

24 times 3.14 is 75.36.

So the surface area is about 75.36 square units.

Let's look back.

First: count the parts.

Then: the base.

Then: the curved side.

Then: add the parts.

Last: about how much.