Cylinder [tex]\( A \)[/tex] has a volume of [tex]\( 360 \, \text{cm}^3 \)[/tex]. Cylinder [tex]\( B \)[/tex] has a base and height identical to that of cylinder [tex]\( A \)[/tex], but leans to the right in such a way that its slant length is greater by 4 cm. What is the volume of cylinder [tex]\( B \)[/tex]?

A. [tex]\( V = 270 \, \text{cm}^3 \)[/tex]
B. [tex]\( V = 360 \, \text{cm}^3 \)[/tex]
C. [tex]\( V = 480 \, \text{cm}^3 \)[/tex]
D. [tex]\( V = 600 \, \text{cm}^3 \)[/tex]



Answer :

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].