Find the slant height $ l $ of a cone if radius $r = 8$ and area $A = 1004.8$.

$l = 31.9797$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 8 $ we have:

$$ AB = 8^2 \cdot \pi $$ $$ AB = 64 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 1004.8 $ and $ AB = 64\pi $ we have:

$$ 1004.8 = 64\pi + CSA $$ $$ CSA = 1004.8 - 64\pi $$ $$ CSA = 803.7381 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 803.7381 $ and $ r = 8 $ we have:

$$ 803.7381 = 8 \cdot l \cdot \pi $$$$ l = \dfrac{ 803.7381 }{ 8 \, \pi} $$$$ l = 31.9797 $$

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