If the basal area of a right cylinder is 144 π and the length of its height is 15cm, what is the lateral area of the cylinder?

1. Calculate the radius of the cylinder using the formula for the area of the base:

\text{Area of base} = \pi r^2 = 144\pi

Divide both sides by $\pi$:

r^2 = 144

Take the square root of both sides:

r = 12 \, \text{cm}

2. Calculate the lateral area of the cylinder using the formula for lateral area:

\text{Lateral area} = 2\pi rh

Substitute the known values ($r = 12\, \text{cm}$ and $h = 15\, \text{cm}$):

\text{Lateral area} = 2\pi (12)(15)

3. Simplify:

\text{Lateral area} = 2\pi \cdot 180

\text{Lateral area} = 360\pi \, \text{cm}^2