STEP 1: find base area $ AB $
To find base area $ AB $ use formula:
$$ AB = r^2 \cdot \pi $$After substituting $ r = 20 $ we have:
$$ AB = 20^2 \cdot \pi $$ $$ AB = 400 \cdot \pi $$STEP 2: find side $ l $
To find side $ l $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $ r = 20 $ and $ h = 99 $ we have:
$$ 20^2 + 99^2 = l^2 $$ $$ 400 + 9801 = l^2 $$ $$ l^2 = 10201 $$ $$ l = \sqrt{ 10201 } $$$$ l = 101 $$STEP 3: find Curved Surface Area $ CSA $
To find Curved Surface Area $ CSA $ use formula:
$$ CSA = r \cdot l \cdot \pi$$After substituting $ r = 20 $ and $ l = 101 $ we have:
$$ CSA = 20 \cdot 101 \cdot \pi$$$$ CSA = 20 \cdot 101 \cdot \pi $$$$ CSA = 2020\pi $$STEP 4: find area $ A $
To find area $ A $ use formula:
$$ A = AB + CSA $$After substituting $ AB = 400\pi $ and $ CSA = 2020\pi $ we have:
$$ A = 400\pi + 2020\pi $$ $$ A = 400\pi + 2020\pi $$ $$ A = 2420\pi $$