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 lateral area $ AL $
To find lateral area $ AL $ use formula:
$$ AL = 2 \cdot r \cdot h \cdot \pi $$After substituting $ r = 4 $ and $ h = 2 $ we have:
$$ AL = 8 \cdot 2 \cdot \pi $$$$ AL = 16\pi $$STEP 3: find area $ A $
To find area $ A $ use formula:
$$ A = 2 AB + AL $$After substituting $ AB = 16\pi $ and $ AL = 16\pi $ we have:
$$ A = 2 \cdot 16\pi + 16\pi $$ $$ A = 32\pi + 16\pi $$ $$ A = 48\pi $$