Area and volume of three-dimensional solids?

Question

How can you use perimeter and area of two-dimensional shapes to find surface area and volume three-dimensional solids?

 

 

Answer 1

Do you have a specific solid in mind?

 

Here is an example of what I think you might be looking for.

 

A cylinder is a solid with a circular base and straight sides. The area of the base can be used to find its volume and surface area and the circumference can be used to find the surface area as well.

 

Recall, for a circle, 

 

C = 2πr and A = πr².

 

The Volume of any cylinder is are area of the base times the height. Let h be the height, then the volume formula is:

 

V = πr²h.

 

The Surface area is the sum of the area of the top and bottom circles plus the area of the lateral side.

 

SA = 2πr² + 2πrh.

 

(The lateral side has area the circumference times the height. This is because, if you cut the side from the top to the bottom, then unroll it like a piece of tin foil, you get a rectangle with length 2πr and height h.)