Find the slant height $ l $ of a cone if radius $r = 24.2$ and area $A = 4802.4416$.

$l = 55.4649$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

$$ AB = r^2 \cdot \pi $$

After substituting $ r = 24.2 $ we have:

$$ AB = 24.2^2 \cdot \pi $$ $$ AB = 585.64 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 4802.4416 $ and $ AB = 585.64\pi $ we have:

$$ 4802.4416 = 585.64\pi + CSA $$ $$ CSA = 4802.4416 - 585.64 $$ $$ CSA = 4216.8016 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 4216.8016 $ and $ r = 24.2 $ we have:

$$ 4216.8016 = 24.2 \cdot l \cdot \pi $$$$ l = \dfrac{ 4216.8016 }{ 24.2 \, \pi} $$$$ l = 55.4649 $$

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