Find the height $ h $ of a cylinder if radius $r = 6$ and area $A = 561.432$.

$h = 8.8924$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 6 $ we have:

$$ AB = 6^2 \cdot \pi $$ $$ AB = 36 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ A = 2 AB + AL $$

After substituting $ A = 561.432 $ and $ AB = 36\pi $ we have:

$$ 561.432 = 2 \cdot 36\pi + AL $$ $$ 561.432 = 72\pi + AL $$ $$ AL = 561.432 - 72\pi $$ $$ AL = 335.2373 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 335.2373 $ and $ r = 6 $ we have:

$$ 335.2373 = 2 \cdot 6 \cdot h \cdot \pi $$$$ 335.2373 = 12 \cdot h \cdot \pi $$$$ h = \dfrac{ 335.2373 }{ 12 \, \pi} $$$$ h = 8.8924 $$

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