STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $r = 2\, \text{cm}$ we have:

$$ AB = \left( 2\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 4\, \text{cm}^2 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $A = 37.68\, \text{cm}$ and $AB = 4\pi\, \text{cm}^2$ we have:

$$ 37.68\, \text{cm} = 4\pi\, \text{cm}^2 + CSA $$ $$ CSA = 37.68\, \text{cm} - 4\pi\, \text{cm}^2 $$ $$ CSA = 25.1136\, \text{cm} $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $CSA = 25.1136\, \text{cm}$ and $r = 2\, \text{cm}$ we have:

$$ 25.1136\, \text{cm} = 2\, \text{cm} \cdot l \cdot \pi $$$$ l = \dfrac{ 25.1136\, \text{cm}}{ 2\, \text{cm} \, \pi } $$$$ l \approx 3.9969 $$

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