Find the slant height $ l $ of a cone if radius $r = 4$ and area $A = 163.28$.

$l = 8.9934$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 4 $ we have:

$$ AB = 4^2 \cdot \pi $$ $$ AB = 16 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 163.28 $ and $ AB = 16\pi $ we have:

$$ 163.28 = 16\pi + CSA $$ $$ CSA = 163.28 - 16\pi $$ $$ CSA = 113.0145 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 113.0145 $ and $ r = 4 $ we have:

$$ 113.0145 = 4 \cdot l \cdot \pi $$$$ l = \dfrac{ 113.0145 }{ 4 \, \pi} $$$$ l = 8.9934 $$

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