Surface Area: Cylinder

Area of 2-D Shapes Review

Area of a Circle = Pi x radius x radius

Area of a Circle = Pi x radius squared

Surface Area of a Cylinder

A cylinder has only 3 surfaces. The two congruent bases and the curved surface.

When you lay the cylinder flat, the curved surface forms a rectangle. The length of the rectangle is the same as the circumference of the base.

In this case the area of the rectangle is 14 times the circumference of the circle or 14 x C.

You'll remember that to find the circumferenceof a circle you multiply the diameter by pi.

Circumference = x diameter

Since the diameter is twice the radius you could also say:

Circumference = x (2 x radius)

or 2r

So the circumference of the base is:

2 x 3.14 x 8 OR 16 x 3.14

C = 50.24 cm

By calculating the circumference of the base we have found the length of the rectangle.

Now you can find the area of the rectangle:

Area = 50.24 x 14 = 703.36 cm2

To find the area of the circular bases:

Area of a circle = r2

Area = 3.14 x 64 = 200.96 cm2

To find the total area of the cylinder we'll add the two bases and the rectangle.

200.96 + 200.96 + 703.36 = 1105.28cm2

Let's just review the steps for the surface area of a cylinder. Keep in mind you'll be finding both the area (r2) and the circumference (D or 2r) of the base.

To find the area of the rectangle:

circumference x height

D x h OR 2r x h (because radius is twice the diameter)

To find the area of the circular base:

Surface area = (2 x area of base) + area of rectangle.

Total surface area 2rh + 2r2

This could also be stated as 2(rh + r2)

Because pi is an irrational number (decimal that never ends or repeats) some of the numbers have been rounded.