Find the slant height $ l $ of a cone if radius $r = 7.9$ and area $A = 667.2814$.

$l = 24.3717$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 7.9 $ we have:

$$ AB = 7.9^2 \cdot \pi $$ $$ AB = 62.41 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 667.2814 $ and $ AB = 62.41\pi $ we have:

$$ 667.2814 = 62.41\pi + CSA $$ $$ CSA = 667.2814 - 62.41 $$ $$ CSA = 604.8714 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 604.8714 $ and $ r = 7.9 $ we have:

$$ 604.8714 = 7.9 \cdot l \cdot \pi $$$$ l = \dfrac{ 604.8714 }{ 7.9 \, \pi} $$$$ l = 24.3717 $$

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