Find the height $ h $ of a cylinder if radius $r = 14$ and area $A = 2110.08$.

$h = 9.9878$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 14 $ we have:

$$ AB = 14^2 \cdot \pi $$ $$ AB = 196 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ A = 2 AB + AL $$

After substituting $ A = 2110.08 $ and $ AB = 196\pi $ we have:

$$ 2110.08 = 2 \cdot 196\pi + AL $$ $$ 2110.08 = 392\pi + AL $$ $$ AL = 2110.08 - 392\pi $$ $$ AL = 878.5757 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 878.5757 $ and $ r = 14 $ we have:

$$ 878.5757 = 2 \cdot 14 \cdot h \cdot \pi $$$$ 878.5757 = 28 \cdot h \cdot \pi $$$$ h = \dfrac{ 878.5757 }{ 28 \, \pi} $$$$ h = 9.9878 $$

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