Find the height $ h $ of a cylinder if radius $r = 3.9$ and area $A = 291.4548$.

$h = 10.6526$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 3.9 $ we have:

$$ AB = 3.9^2 \cdot \pi $$ $$ AB = 15.21 \cdot \pi $$

STEP 2: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ A = 2 AB + AL $$

After substituting $ A = 291.4548 $ and $ AB = 15.21\pi $ we have:

$$ 291.4548 = 2 \cdot 15.21\pi + AL $$ $$ 291.4548 = 30.42 + AL $$ $$ AL = 291.4548 - 30.42 $$ $$ AL = 261.0348 $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $ AL = 261.0348 $ and $ r = 3.9 $ we have:

$$ 261.0348 = 2 \cdot 3.9 \cdot h \cdot \pi $$$$ 261.0348 = 7.8 \cdot h \cdot \pi $$$$ h = \dfrac{ 261.0348 }{ 7.8 \, \pi} $$$$ h = 10.6526 $$

Cylinder Calculator