To solve this problem, we'll need to start by understanding certain key properties about cylinders and the relationship between volume, base area, and height.
First, let's recall how the volume of a cylinder is calculated. The volume [tex]\( V \)[/tex] of a cylinder is determined using the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base of the cylinder.
- [tex]\( h \)[/tex] is the height of the cylinder.
We are given that cylinder A has a volume of [tex]\( 360 \, \text{cm}^3 \)[/tex]. For cylinder B, although it leans to the right and its slant length increases by 4 cm, the base area [tex]\(\pi r^2\)[/tex] and the vertical height [tex]\( h \)[/tex] of cylinder B are identical to those of cylinder A.
Since the base area and the height of cylinder B are the same as those of cylinder A, and the volume of a cylinder depends solely on these two parameters, the volume of cylinder B will remain the same as the volume of cylinder A.
Thus, the volume of cylinder B is also [tex]\( 360 \, \text{cm}^3 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{V = 360 \, \text{cm}^3} \][/tex]
This corresponds to option [tex]\( \text{B} \)[/tex].
