Find the height $ h $ of a cylinder if radius $r = 16$ and area $A = 2833.536$.

$h = 12.1857$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 16 $ we have:

$$ AB = 16^2 \cdot \pi $$ $$ AB = 256 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ A = 2 AB + AL $$

After substituting $ A = 2833.536 $ and $ AB = 256\pi $ we have:

$$ 2833.536 = 2 \cdot 256\pi + AL $$ $$ 2833.536 = 512\pi + AL $$ $$ AL = 2833.536 - 512\pi $$ $$ AL = 1225.0406 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 1225.0406 $ and $ r = 16 $ we have:

$$ 1225.0406 = 2 \cdot 16 \cdot h \cdot \pi $$$$ 1225.0406 = 32 \cdot h \cdot \pi $$$$ h = \dfrac{ 1225.0406 }{ 32 \, \pi} $$$$ h = 12.1857 $$

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