Question

How do I find the surface area and volume of any shape?

Answer 1

Answer:

Step-by-step explanation:For any shape it’s always true that for volume

V

the surface area is:      =2‾‾‾√3

for some constant   depending on the shape. So to work out the surface area from the volume we just need to know the value of   for the shape in the question.

For a cube for example we have that  =6, assuming consistent units i.e.: unit 2 for area and unit 3

3

 for volume.

More generally if we have formula for both volume and surface area in terms of a particular one dimensional measurement  

d

 of the shape then we can always write these formula in the form:

 

=13

=12

for constants  constants   1  and  1

. Then we have:

=1‾‾‾√3

=1(1)2‾‾‾‾‾‾√3

=121‾‾‾√32‾‾‾√3

and therefore:

=121‾‾‾√3

For example for a sphere we have that   that  =42  and  =433 and therefore:

=4(43)2‾‾‾‾‾‾√3

=36‾‾‾‾√3

So if a particular sphere has volume   =8  then we can calculate its surface area to be:

=36‾‾‾‾√382‾‾√3=436‾‾‾‾√3 m2