Find the height $ h $ of a cylinder if radius $r = 5$ and area $A = 298.3$.

$h = 4.4952$

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:

$$ A = 2 AB + AL $$

After substituting $ A = 298.3 $ and $ AB = 25\pi $ we have:

$$ 298.3 = 2 \cdot 25\pi + AL $$ $$ 298.3 = 50\pi + AL $$ $$ AL = 298.3 - 50\pi $$ $$ AL = 141.2204 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 141.2204 $ and $ r = 5 $ we have:

$$ 141.2204 = 2 \cdot 5 \cdot h \cdot \pi $$$$ 141.2204 = 10 \cdot h \cdot \pi $$$$ h = \dfrac{ 141.2204 }{ 10 \, \pi} $$$$ h = 4.4952 $$

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