Answer:
220.5π cm³ ≈ 692.72 cm³
Step-by-step explanation:
You want the volume of a cylinder of height 12.5 cm, given that its lateral area is 105π cm².
Radius
The lateral area of the cylinder is given by ...
LA = 2πrh
Solving for r, we have ...
105π = 2πr·12.5
r = 105/25 = 4.2 . . . . . cm
Volume
The volume is given by ...
V = πr²h
V = p(4.2 cm)²(12.5 cm) = 220.5π cm³
The volume of the cylinder is 220.5π cm³ ≈ 692.72 cm³.
