STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $r = 5.13\, \text{cm}$ we have:

$$ AB = \left( 5.13\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 26.3169\, \text{cm}^2 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $A = 98\, \text{cm}$ and $AB = 26.3169\pi\, \text{cm}^2$ we have:

$$ 98\, \text{cm} = 26.3169\pi\, \text{cm}^2 + CSA $$ $$ CSA = 98\, \text{cm} - 26.3169\, \text{cm}^2 $$ $$ CSA = 71.6831\, \text{cm} $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $CSA = 71.6831\, \text{cm}$ and $r = 5.13\, \text{cm}$ we have:

$$ 71.6831\, \text{cm} = 5.13\, \text{cm} \cdot l \cdot \pi $$$$ l = \dfrac{ 71.6831\, \text{cm}}{ 5.13\, \text{cm} \, \pi } $$$$ l \approx 4.4478 $$

STEP 4: find side $ h $

To find side $ h $ use Pythagorean Theorem:

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

After substituting $r = 5.13\, \text{cm}$ and $l = 4.4478\, \text{cm}^0$ we have:

$$ \left( 5.13\, \text{cm} \right)^{2} + h^2 = 4.4478 $$ $$ h^2 = 4.4478 - \left( 5.13\, \text{cm} \right)^{2} $$ $$ h^2 = 19.7832 - 26.3169\, \text{cm}^2 $$ $$ h^2 = -6.5337 $$

This equation has no solution $ \Longrightarrow $ The problem has no solution.

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