STEP 1: find height $ h $

To find height $ h $ use formula:

$$ V = \dfrac{ a ^{ 2 } \cdot h }{ 3 } $$

After substituting $V = 500\, \text{cm}$ and $a = 10\, \text{cm}$ we have:

$$ 500\, \text{cm} = \dfrac{ 10\, \text{cm} ^{ 2 } \cdot h }{ 3 } $$$$ 500\, \text{cm} \cdot 3 = 10\, \text{cm} ^{ 2 } \cdot h $$$$ 1500\, \text{cm} = 100\, \text{cm}^2 \cdot h $$$$ h = \dfrac{ 1500\, \text{cm} }{ 100\, \text{cm}^2 } $$$$ h = 15\, \text{cm}^-1 $$

STEP 2: find slant height $ s $

To find slant height $ s $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $h = 15\, \text{cm}^-1$ and $a = 10\, \text{cm}$ we have:

$$ \left( 15\, \text{cm}^-1 \right)^{2} + \frac{ \left( 10\, \text{cm} \right)^{2} }{ 4 }= s^2 $$ $$ 225\, \text{cm}^-2 + \frac{ 100\, \text{cm}^2 }{ 4 }= s^2 $$ $$ 225\, \text{cm}^-2 + 25\, \text{cm}^2 = s^2 $$ $$ s^2 = 250\, \text{cm}^-2 $$ $$ s = \sqrt{ 250\, \text{cm}^-2 } $$$$ s = 5 \sqrt{ 10 }\, \text{cm}^-1 $$

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