Find the height $ h $ of a cylinder if radius $r = 8$ and area $A = 653.12$.

$h = 4.9934$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 8 $ we have:

$$ AB = 8^2 \cdot \pi $$ $$ AB = 64 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ A = 2 AB + AL $$

After substituting $ A = 653.12 $ and $ AB = 64\pi $ we have:

$$ 653.12 = 2 \cdot 64\pi + AL $$ $$ 653.12 = 128\pi + AL $$ $$ AL = 653.12 - 128\pi $$ $$ AL = 250.9961 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 250.9961 $ and $ r = 8 $ we have:

$$ 250.9961 = 2 \cdot 8 \cdot h \cdot \pi $$$$ 250.9961 = 16 \cdot h \cdot \pi $$$$ h = \dfrac{ 250.9961 }{ 16 \, \pi} $$$$ h = 4.9934 $$

Cylinder Calculator