Find the area $ A $ of a cylinder if height $h = 3.4$ and base area $AB = 5.6$.

$A = 20.2788$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

After substituting $ AB = 5.6 $ we have:

$$ AB = r^2 \cdot \pi $$ $$ r^2 \cdot \pi = 5.6 $$ $$ r = \sqrt{ \frac{ 5.6 }{\pi} } $$ $$ r \approx 1.3351 $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

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

After substituting $ r = 1.3351 $ and $ h = 3.4 $ we have:

$$ AL = 2.6702 \cdot 3.4 \cdot \pi $$$$ AL = 9.0788\pi $$

STEP 3: find area $ A $

To find area $ A $ use formula:

$$ A = 2 AB + AL $$

After substituting $ AB = 5.6 $ and $ AL = 9.0788\pi $ we have:

$$ A = 2 \cdot 5.6 + 9.0788\pi $$ $$ A = 11.2 + 9.0788 $$ $$ A = 20.2788 $$

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