The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the cylinder and h is the height of the cylinder. Since Cylinder B has half the diameter of Cylinder A, its radius is half that of Cylinder A.
Let's say that the radius of Cylinder A is r and its height is h. The radius of Cylinder B would be r/2, since it has half the diameter of Cylinder A. The height of Cylinder B is the same as that of Cylinder A, so it is also h.
So, the volume of Cylinder A is:
V(A) = πr^2h
And the volume of Cylinder B is:
V(B) = π(r/2)^2h
Simplifying the equation for V(B):
V(B) = π(r^2/4)h
We can simplify further by multiplying both sides by 4/4:
V(B) = (4/4)π(r^2/4)h
V(B) = π(r^2/4)(4h)
V(B) = πr^2h/4
Therefore, the expression that presents the volume of Cylinder B in terms of the volume of Cylinder A is:
V(B) = V(A)/4