Find the Curved Surface Area $ CSA $ of a cone if radius $r = 4\, \text{cm}$ and height $h = \sqrt{ 273 }\, \text{cm}$.

$68\pi\, \text{cm}^2$

STEP 1: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $r = 4\, \text{cm}$ and $h = \sqrt{ 273 }\, \text{cm}$ we have:

$$ \left( 4\, \text{cm} \right)^{2} + \left( \sqrt{ 273 }\, \text{cm} \right)^{2} = l^2 $$ $$ 16\, \text{cm}^2 + 273\, \text{cm}^2 = l^2 $$ $$ l^2 = 289\, \text{cm}^2 $$ $$ l = \sqrt{ 289\, \text{cm}^2 } $$$$ l = 17\, \text{cm} $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $r = 4\, \text{cm}$ and $l = 17\, \text{cm}$ we have:

$$ CSA = 17\, \text{cm} \cdot 4\, \text{cm} \cdot \pi$$$$ CSA = 17\, \text{cm} \cdot 4\, \text{cm} \cdot \pi $$$$ CSA = 68\pi\, \text{cm}^2 $$

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