Find the slant height $ l $ of a cone if radius $r = 7$ and area $A = 505.54$.

$l = 15.9883$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 7 $ we have:

$$ AB = 7^2 \cdot \pi $$ $$ AB = 49 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 505.54 $ and $ AB = 49\pi $ we have:

$$ 505.54 = 49\pi + CSA $$ $$ CSA = 505.54 - 49\pi $$ $$ CSA = 351.602 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 351.602 $ and $ r = 7 $ we have:

$$ 351.602 = 7 \cdot l \cdot \pi $$$$ l = \dfrac{ 351.602 }{ 7 \, \pi} $$$$ l = 15.9883 $$

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