STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $r = 4\, \text{cm}$ we have:

$$ AB = \left( 4\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 16\, \text{cm}^2 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $A = 163.28\, \text{cm}$ and $AB = 16\pi\, \text{cm}^2$ we have:

$$ 163.28\, \text{cm} = 16\pi\, \text{cm}^2 + CSA $$ $$ CSA = 163.28\, \text{cm} - 16\pi\, \text{cm}^2 $$ $$ CSA = 113.0145\, \text{cm} $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $CSA = 113.0145\, \text{cm}$ and $r = 4\, \text{cm}$ we have:

$$ 113.0145\, \text{cm} = 4\, \text{cm} \cdot l \cdot \pi $$$$ l = \dfrac{ 113.0145\, \text{cm}}{ 4\, \text{cm} \, \pi } $$$$ l \approx 8.9934 $$

Cone Calculator