Find the slant height $ l $ of a cone if radius $r = 5$ and area $A = 290.6$.

$l = 13.5002$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 5 $ we have:

$$ AB = 5^2 \cdot \pi $$ $$ AB = 25 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 290.6 $ and $ AB = 25\pi $ we have:

$$ 290.6 = 25\pi + CSA $$ $$ CSA = 290.6 - 25\pi $$ $$ CSA = 212.0602 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 212.0602 $ and $ r = 5 $ we have:

$$ 212.0602 = 5 \cdot l \cdot \pi $$$$ l = \dfrac{ 212.0602 }{ 5 \, \pi} $$$$ l = 13.5002 $$

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