Hopefully you said [math]s^3[/math], or s^3 if you did not use the math editor.

One of the other dimensions needs to be halved, and the other should stay the same.

Yes. For example the prism with dimensions 4x4x5 and the prism with dimensions 4x2x8 both have a surface area of 112 square units.[br][br]For a prism with dimensions a,b,c to have the same surface area as a prism with dimensions d,e,f they would need to have the following:[br]1. ab + ac + bc = de + df + ef[br]2. For different dimensions, we could say that holds true so long as a [math]\ne[/math] d.[br]There are many numbers a,b,c,d,e,f where these two properties are true.

1. The surface area increases, specifically by a factor of [math]\frac{ab+ac+bc}{3ab+3ac+bc}[/math], [math]\frac{ab+ac+bc}{3ab+ac+3bc}[/math], or [math]\frac{ab+ac+bc}{ac+3ac+3bc}[/math]. So yes, it does matter which dimension is tripled since [math]3ab+3ac+bc[/math], [math]3ab+ac+3bc[/math], and [math]ab+3ac+3bc[/math] are not necessarily equal.[br][br]2. The volume will quadruple (i.e. increase by a factor of 4). Since, [math]V=\left(2a\right)\left(2b\right)c=4abc[/math].

[math]2\pi r[/math] or 2*pi*r, where [i]r[/i] is the radius of the circle.

The area will increase by a factor of ~2. (Exact number not important since there isn't an easy pattern.)[br]The perimeter will increase by 3 (the side length).

[i]sn[/i]

The area will increase. The exact factor is not important.[br]The perimeter will increase by 10 units. Since we added 2 sides of length 5 units each, we added 2*5 = 10 units to the perimeter.

In both cases the volume will increase. You can test below at a few different heights and compare how the volume changed between each increase. And you can do the same with changing the radius.