STEP 1: find side $ h $

To find side $ h $ use Pythagorean Theorem:

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

After substituting $r = 8\, \text{cm}$ and $l = 17\, \text{cm}$ we have:

$$ \left( 8\, \text{cm} \right)^{2} + h^2 = \left( 17\, \text{cm} \right)^{2} $$ $$ h^2 = \left( 17\, \text{cm} \right)^{2} - \left( 8\, \text{cm} \right)^{2} $$ $$ h^2 = 289\, \text{cm}^2 - 64\, \text{cm}^2 $$ $$ h^2 = 225\, \text{cm}^2 $$ $$ h = \sqrt{ 225\, \text{cm}^2 } $$$$ h = 15\, \text{cm} $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

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

After substituting $r = 8\, \text{cm}$ and $h = 15\, \text{cm}$ we have:

$$ V = \dfrac{ 225\, \text{cm}^2 \cdot 8\, \text{cm} \cdot \pi}{ 3 }$$$$ V = \dfrac{ 1800\, \text{cm}^3 \, \pi}{ 3 } $$$$ V = 600\pi\, \text{cm}^3 $$

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