How do you find the surface area of a opened top cylinder?

Question

I am trying to find the Surface area of a cylinder with a opened top with H=4cm and R= 2cm

Answer 1

Surface area of a  cylinder is:  2πrh + 2πr²

 

r = radius,   h = height

 

2πrh will be the surface area around the cylinder

 

2πr² will be the surface area of the two ends (circles)

 

Since one end is missing, you only use πr²

 

Surface Area is:

 

2π(2cm)(4cm) + π(2²cm)

 

16πcm² + 4πcm² 

 

20πcm² = 62.8 cm²

Answer 2

An open top cylinder has a rounded surface plus one circular base.    If you were to unwrap the rounded surface, you get a flat rectangular shape.

 

The area of a circle is  πr².

The area of the rectangular shape is   2πrh.   The 2πr comes from the unwrapped side.

 

Combine these areas to get

 

SA = πr² + 2πrh

 

Answer 3

Surface area is the label on the can.

a = Ch, where C = circumference, h = height

a = 4π4

a = 16π