Find the area $ A $ of a cone if radius $r = 11$ and height $h = 15$.

$A = 1022.9397$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 11 $ we have:

$$ AB = 11^2 \cdot \pi $$ $$ AB = 121 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

$$ r^2 + h^2 = l^2 $$

After substituting $ r = 11 $ and $ h = 15 $ we have:

$$ 11^2 + 15^2 = l^2 $$ $$ 121 + 225 = l^2 $$ $$ l^2 = 346 $$ $$ l = \sqrt{ 346 } $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ CSA = r \cdot l \cdot \pi$$

After substituting $ r = 11 $ and $ l = \sqrt{ 346 } $ we have:

$$ CSA = 11 \cdot \sqrt{ 346 } \cdot \pi$$$$ CSA = 11 \cdot \sqrt{ 346 } \cdot \pi $$$$ CSA = 11 \sqrt{ 346 }\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 121\pi $ and $ CSA = 11 \sqrt{ 346 }\pi $ we have:

$$ A = 121\pi + 11 \sqrt{ 346 }\pi $$ $$ A = 121\pi + 11 \sqrt{ 346 }\pi $$ $$ A = 1022.9397 $$

Cone Calculator