STEP 1: find side $ l $

To find side $ l $ use Pythagorean Theorem:

$$ r^2 + h^2 = l^2 $$

After substituting $r = 3.9\, \text{cm}$ and $h = 12\, \text{cm}$ we have:

$$ \left( 3.9\, \text{cm} \right)^{2} + \left( 12\, \text{cm} \right)^{2} = l^2 $$ $$ 15.21\, \text{cm}^2 + 144\, \text{cm}^2 = l^2 $$ $$ l^2 = 159.21\, \text{cm}^2 $$ $$ l = \sqrt{ 159.21\, \text{cm}^2 } $$$$ l = 12.6178\, \text{cm} $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ CSA = l \cdot r \cdot \pi$$

After substituting $r = 3.9\, \text{cm}$ and $l = 12.6178\, \text{cm}$ we have:

$$ CSA = 12.6178\, \text{cm} \cdot 3.9\, \text{cm} \cdot \pi$$$$ CSA = 12.6178\, \text{cm} \cdot 3.9\, \text{cm} \cdot \pi $$$$ CSA = 49.2096\pi\, \text{cm}^2 $$

Cone Calculator