Find the height $ h $ of a cylinder if radius $r = 7.2$ and area $A = 899.7984$.

$h = 17.5981$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 7.2 $ we have:

$$ AB = 7.2^2 \cdot \pi $$ $$ AB = 51.84 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ A = 2 AB + AL $$

After substituting $ A = 899.7984 $ and $ AB = 51.84\pi $ we have:

$$ 899.7984 = 2 \cdot 51.84\pi + AL $$ $$ 899.7984 = 103.68 + AL $$ $$ AL = 899.7984 - 103.68 $$ $$ AL = 796.1184 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 796.1184 $ and $ r = 7.2 $ we have:

$$ 796.1184 = 2 \cdot 7.2 \cdot h \cdot \pi $$$$ 796.1184 = 14.4 \cdot h \cdot \pi $$$$ h = \dfrac{ 796.1184 }{ 14.4 \, \pi} $$$$ h = 17.5981 $$

Cylinder Calculator