STEP 1: find side $ r $

To find side $ r $ use Pythagorean Theorem:

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

After substituting $h = 5\, \text{cm}$ and $l = 9.5\, \text{cm}$ we have:

$$ r ^ {\,2} + \left( 5\, \text{cm} \right)^{2} = \left( 9.5\, \text{cm} \right)^{2} $$ $$ r ^ {\,2} = \left( 9.5\, \text{cm} \right)^{2} - \left( 5\, \text{cm} \right)^{2} $$ $$ r ^ {\,2} = 90.25\, \text{cm}^2 - 25\, \text{cm}^2 $$ $$ r ^ {\,2} = 65.25\, \text{cm}^2 $$ $$ r = \sqrt{ 65.25\, \text{cm}^2 } $$$$ r = 8.0777\, \text{cm} $$

STEP 2: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $r = 8.0777\, \text{cm}$ we have:

$$ AB = \left( 8.0777\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 65.25\, \text{cm}^2 \cdot \pi $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $r = 8.0777\, \text{cm}$ and $l = 9.5\, \text{cm}$ we have:

$$ CSA = 9.5\, \text{cm} \cdot 8.0777\, \text{cm} \cdot \pi$$$$ CSA = 9.5\, \text{cm} \cdot 8.0777\, \text{cm} \cdot \pi $$$$ CSA = 76.7386\pi\, \text{cm}^2 $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $AB = 65.25\pi\, \text{cm}^2$ and $CSA = 76.7386\pi\, \text{cm}^2$ we have:

$$ A = 65.25\pi\, \text{cm}^2 + 76.7386\pi\, \text{cm}^2 $$ $$ A = 65.25\, \text{cm}^2 + 76.7386\, \text{cm}^2 $$ $$ A = 141.9886\, \text{cm}^2 $$

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