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Surface area
Surface area of cylinders

A cylinder is a 3-dimensional figure with two circular bases and a curved face.

The surface area of a cylinder the sum of the areas of its two bases and its curved face.
To conceptualize surface area of cylinders, we can imagine that the lateral area of a cylinder can be "unrolled" into a rectangle with one side equaling the circumference of the circle and the other side equal to the height of the cylinder (unless it is oblique).

It is pretty easy to calculate their areas and then add them up.

SAcylinder=

What is the surface area of this cylinder? Use π ≈ 3.14.

Remember that

Surface area of a cylinder:

 Surface area = Atop + Abottom + Aside

Find the radius and height of the cylinder.

 height = 4

Find the area of the circle on the top of the cylinder. Use 3.14 for π.

Atop = πr2

3.14 ×
 5 × 5

78.5

The circle on the bottom of the cylinder is the same, so:

Abottom =
 Atop ≈ 78.5

Find the circumference of the top circle.

C = r

2 ×
 3.14 × 5

31.4

Now find the area of the curved surface. The curved surface is a rectangle. One side length is the height, and the other side length is the circumference of the circle.

Aside =
 C × h

 31.4 × 4

125.6

Now add the areas to find the surface area of the cylinder.

Surface area = Atop + Abottom + Aside

78.5 +
 78.5 + 125.6

282.6

The surface area of the cylinder is about 282.6 square millimeters.

What is the surface area of this cylinder when r=3, and h=6?

Use π ≈ 3.14.