STEP 1: find base area $ AB $
To find base area $ AB $ use formula:
$$ AB = r^2 \cdot \pi $$After substituting $ r = 4 $ we have:
$$ AB = 4^2 \cdot \pi $$ $$ AB = 16 \cdot \pi $$STEP 2: find side $ l $
To find side $ l $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $ r = 4 $ and $ h = 2 $ we have:
$$ 4^2 + 2^2 = l^2 $$ $$ 16 + 4 = l^2 $$ $$ l^2 = 20 $$ $$ l = \sqrt{ 20 } $$$$ l = 2 \sqrt{ 5 } $$STEP 3: find Curved Surface Area $ CSA $
To find Curved Surface Area $ CSA $ use formula:
$$ CSA = r \cdot l \cdot \pi$$After substituting $ r = 4 $ and $ l = 2 \sqrt{ 5 } $ we have:
$$ CSA = 4 \cdot 2 \sqrt{ 5 } \cdot \pi$$$$ CSA = 4 \cdot 2 \sqrt{ 5 } \cdot \pi $$$$ CSA = 8 \sqrt{ 5 }\pi $$STEP 4: find area $ A $
To find area $ A $ use formula:
$$ A = AB + CSA $$After substituting $ AB = 16\pi $ and $ CSA = 8 \sqrt{ 5 }\pi $ we have:
$$ A = 16\pi + 8 \sqrt{ 5 }\pi $$ $$ A = 16\pi + 8 \sqrt{ 5 }\pi $$ $$ A = 106.464 $$