## Answer :

**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**.