Question

A prism has total surface area of 360 m2 and volume of 60 m3.
If the length, width, and height are reduced to half their original sizes, what will be the following?
a.) the new surface area
b.) the new volume

Also, while I'm asking, how would you go about doing the same thing, but instead of reducing the size of the prism, you multiply it?

Answer 1

S=width*length*height
\[S'=\frac{ width }{ 2 }\times \frac{ length }{ 2 }\times \frac{ height }{ 2 }=\frac{ S }{ 8 }\]
A=width*length
\[A'=\frac{ width }{ 2 }\times \frac{ length }{ 2 }=\frac{ A }{ ? }\]

Answer 2

Why is the S divided by 8?

Answer 3

2*2*2=8

Answer 4

Thing is, I'm not given the dimensions of the prism, so I can't use this.