Find the slant height $ l $ of a cone if radius $r = 9.6$ and area $A = 1178.6304$.

$l = 36.0244$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 9.6 $ we have:

$$ AB = 9.6^2 \cdot \pi $$ $$ AB = 92.16 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 1178.6304 $ and $ AB = 92.16\pi $ we have:

$$ 1178.6304 = 92.16\pi + CSA $$ $$ CSA = 1178.6304 - 92.16 $$ $$ CSA = 1086.4704 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 1086.4704 $ and $ r = 9.6 $ we have:

$$ 1086.4704 = 9.6 \cdot l \cdot \pi $$$$ l = \dfrac{ 1086.4704 }{ 9.6 \, \pi} $$$$ l = 36.0244 $$

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