Surface area of cylinder radius 3 height 5

Step by step

The question

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

1 Count the parts

The surface area is the area of all the outside.

A cylinder has a circle on top and a circle at the bottom.

Cut the curved side and roll it out flat: it is a rectangle.

2 The two circles

One circle is π × r².

There are two of them.

Now put the numbers in: r = 3.

3² means 3 times 3.

That is 9.

2 times 9 is 18.

So the two circles are 18π.

3 The curved side

The rectangle is as high as the cylinder: 5.

Its length goes once around the circle: 2 × π × r.

π is a special number for circles.

It is about 3.14.

So the side is around times height: 2 × π × r × h.

Now put the numbers in: r = 3 and h = 5.

2 times 3 times 5 is 30.

So the side is 30π.

4 Add the parts

Now we add the two circles and the side.

18 plus 30 is 48.

So S = 48π.

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.

48 times 3.14 is 150.72.

So the surface area is about 150.72 square units.

Let's look back.

First: count the parts.

Then: the two circles.

Then: the curved side.

Then: add the parts.

Last: about how much.