Find the area $ A $ of a cone if height $h = 5$ and slant height $l = 9.5$.

$A = 141.9886$

STEP 1: find side $ r $

To find side $ r $ use Pythagorean Theorem:

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

After substituting $ h = 5 $ and $ l = 9.5 $ we have:

$$ r ^ {\,2} + 5^2 = 9.5^2 $$ $$ r ^ {\,2} = 9.5^2 - 5^2 $$ $$ r ^ {\,2} = 90.25 - 25 $$ $$ r ^ {\,2} = 65.25 $$ $$ r = \sqrt{ 65.25 } $$$$ r = 8.0777 $$

STEP 2: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 8.0777 $ we have:

$$ AB = 8.0777^2 \cdot \pi $$ $$ AB = 65.25 \cdot \pi $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 8.0777 $ and $ l = 9.5 $ we have:

$$ CSA = 8.0777 \cdot 9.5 \cdot \pi$$$$ CSA = 8.0777 \cdot 9.5 \cdot \pi $$$$ CSA = 76.7386\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 65.25\pi $ and $ CSA = 76.7386\pi $ we have:

$$ A = 65.25\pi + 76.7386\pi $$ $$ A = 65.25 + 76.7386 $$ $$ A = 141.9886 $$

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