Find the slant height $ l $ of a cone if radius $r = 13$ and area $A = 1918.54$.

$l = 33.9762$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 13 $ we have:

$$ AB = 13^2 \cdot \pi $$ $$ AB = 169 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 1918.54 $ and $ AB = 169\pi $ we have:

$$ 1918.54 = 169\pi + CSA $$ $$ CSA = 1918.54 - 169\pi $$ $$ CSA = 1387.6108 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 1387.6108 $ and $ r = 13 $ we have:

$$ 1387.6108 = 13 \cdot l \cdot \pi $$$$ l = \dfrac{ 1387.6108 }{ 13 \, \pi} $$$$ l = 33.9762 $$

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