STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $r = 3\, \text{cm}$ we have:

$$ AB = \left( 3\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 9\, \text{cm}^2 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $A = 24\, \text{cm}$ and $AB = 9\pi\, \text{cm}^2$ we have:

$$ 24\, \text{cm} = 9\pi\, \text{cm}^2 + CSA $$ $$ CSA = 24\, \text{cm} - 9\pi\, \text{cm}^2 $$ $$ CSA = -4.2743\, \text{cm} $$

The result has to be greater than zero. $ \Longrightarrow $ The problem has no solution.

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