Find the height $ h $ of a cylinder if radius $r = 9$ and area $A = 842.148$.

$h = 5.8924$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 9 $ we have:

$$ AB = 9^2 \cdot \pi $$ $$ AB = 81 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ A = 2 AB + AL $$

After substituting $ A = 842.148 $ and $ AB = 81\pi $ we have:

$$ 842.148 = 2 \cdot 81\pi + AL $$ $$ 842.148 = 162\pi + AL $$ $$ AL = 842.148 - 162\pi $$ $$ AL = 333.21 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 333.21 $ and $ r = 9 $ we have:

$$ 333.21 = 2 \cdot 9 \cdot h \cdot \pi $$$$ 333.21 = 18 \cdot h \cdot \pi $$$$ h = \dfrac{ 333.21 }{ 18 \, \pi} $$$$ h = 5.8924 $$

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