Find the height $ h $ of a cylinder if radius $r = 16.3$ and area $A = 2518.1544$.

$h = 19.3991$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 16.3 $ we have:

$$ AB = 16.3^2 \cdot \pi $$ $$ AB = 265.69 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ A = 2 AB + AL $$

After substituting $ A = 2518.1544 $ and $ AB = 265.69\pi $ we have:

$$ 2518.1544 = 2 \cdot 265.69\pi + AL $$ $$ 2518.1544 = 531.38 + AL $$ $$ AL = 2518.1544 - 531.38 $$ $$ AL = 1986.7744 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 1986.7744 $ and $ r = 16.3 $ we have:

$$ 1986.7744 = 2 \cdot 16.3 \cdot h \cdot \pi $$$$ 1986.7744 = 32.6 \cdot h \cdot \pi $$$$ h = \dfrac{ 1986.7744 }{ 32.6 \, \pi} $$$$ h = 19.3991 $$

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