Find the area $ A $ of a cylinder if radius $r = 5$ and height $h = 4$.

$A = 90\pi$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 5 $ we have:

$$ AB = 5^2 \cdot \pi $$ $$ AB = 25 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ AL = 2 \cdot r \cdot h \cdot \pi $$

After substituting $ r = 5 $ and $ h = 4 $ we have:

$$ AL = 10 \cdot 4 \cdot \pi $$$$ AL = 40\pi $$

STEP 3: find area $ A $

To find area $ A $ use formula:

$$ A = 2 AB + AL $$

After substituting $ AB = 25\pi $ and $ AL = 40\pi $ we have:

$$ A = 2 \cdot 25\pi + 40\pi $$ $$ A = 50\pi + 40\pi $$ $$ A = 90\pi $$

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