STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $r = 19\, \text{cm}$ we have:

$$ AB = \left( 19\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 361\, \text{cm}^2 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $A = 3490.11\, \text{cm}$ and $AB = 361\pi\, \text{cm}^2$ we have:

$$ 3490.11\, \text{cm} = 361\pi\, \text{cm}^2 + CSA $$ $$ CSA = 3490.11\, \text{cm} - 361\pi\, \text{cm}^2 $$ $$ CSA = 2355.9951\, \text{cm} $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $CSA = 2355.9951\, \text{cm}$ and $r = 19\, \text{cm}$ we have:

$$ 2355.9951\, \text{cm} = 19\, \text{cm} \cdot l \cdot \pi $$$$ l = \dfrac{ 2355.9951\, \text{cm}}{ 19\, \text{cm} \, \pi } $$$$ l \approx 39.4703 $$

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