Find the slant height $ l $ of a cone if radius $r = 19$ and area $A = 2762.258$.

$l = 27.2765$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 19 $ we have:

$$ AB = 19^2 \cdot \pi $$ $$ AB = 361 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 2762.258 $ and $ AB = 361\pi $ we have:

$$ 2762.258 = 361\pi + CSA $$ $$ CSA = 2762.258 - 361\pi $$ $$ CSA = 1628.1431 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 1628.1431 $ and $ r = 19 $ we have:

$$ 1628.1431 = 19 \cdot l \cdot \pi $$$$ l = \dfrac{ 1628.1431 }{ 19 \, \pi} $$$$ l = 27.2765 $$

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