A wooden cylinder of height 8 cm and radius 3 cm is cut in two along a vertical axis of symmetry. Calculate the total surface area of the two pieces.

Question

Algebra with Surface area.

Answer 1

The surface are of a cylinder is

 

SA = 2πr² + 2πrh

 

where:

r = radius

h = height

 

This formula comes from adding the areas of the surfaces of the cylinder.  It has two flat circular faces and a rounded face.

 

If we cut the cylinder from the circular face symmetrically, the surface area for one piece will be

 

SA = 2[(πr²)/2]  +  (2πr/2)h  +  2rh

 

We will have 2-half flat circular faces, a flat rectangular surface, and half of the rounded surface.

 

Simplify the SA formula.

 

SA = πr² + πrh + 2rh

SA = r(πr + πh + 2h)

 

Substitute the values into this formula.

 

SA = 3(3π + 8π + (2*8))

SA = 3(11π + 16)

SA = 33π + 48

SA = 151.67 cm²

 

Since we have 2 pieces, multiply this result by 2.

 

2(151.67 cm²) = 303.34 cm².

 

The total area is 303.34 cm².