STEP 1: find base area $ AB $
To find base area $ AB $ use formula:
$$ AB = r^2 \cdot \pi $$After substituting $r = 5\, \text{cm}$ we have:
$$ AB = \left( 5\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 25\, \text{cm}^2 \cdot \pi $$STEP 2: find Curved Surface Area $ CSA $
To find Curved Surface Area $ CSA $ use formula:
$$ A = AB + CSA $$After substituting $A = 542.87\, \text{cm}$ and $AB = 25\pi\, \text{cm}^2$ we have:
$$ 542.87\, \text{cm} = 25\pi\, \text{cm}^2 + CSA $$ $$ CSA = 542.87\, \text{cm} - 25\pi\, \text{cm}^2 $$ $$ CSA = 464.3302\, \text{cm} $$STEP 3: find slant height $ l $
To find slant height $ l $ use formula:
$$ CSA = l \cdot r \cdot \pi$$After substituting $CSA = 464.3302\, \text{cm}$ and $r = 5\, \text{cm}$ we have:
$$ 464.3302\, \text{cm} = 5\, \text{cm} \cdot l \cdot \pi $$$$ l = \dfrac{ 464.3302\, \text{cm}}{ 5\, \text{cm} \, \pi } $$$$ l \approx 29.5601 $$