Find the slant height $ l $ of a cone if radius $r = 26$ and area $A = 5363.748$.

$l = 39.6667$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 26 $ we have:

$$ AB = 26^2 \cdot \pi $$ $$ AB = 676 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 5363.748 $ and $ AB = 676\pi $ we have:

$$ 5363.748 = 676\pi + CSA $$ $$ CSA = 5363.748 - 676\pi $$ $$ CSA = 3240.0314 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 3240.0314 $ and $ r = 26 $ we have:

$$ 3240.0314 = 26 \cdot l \cdot \pi $$$$ l = \dfrac{ 3240.0314 }{ 26 \, \pi} $$$$ l = 39.6667 $$

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