Find the height $ h $ of a cone if diameter $d = 8\, \text{cm}$ and slant height $l = 17\, \text{cm}$.

$\sqrt{ 273 }\, \text{cm}$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $d = 8\, \text{cm}$ we have:

$$ 8\, \text{cm} = 2 \cdot r $$ $$ r = \dfrac{ 8\, \text{cm} }{ 2 } $$ $$ r = 4\, \text{cm} $$

STEP 2: find side $ h $

To find side $ h $ use Pythagorean Theorem:

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

After substituting $r = 4\, \text{cm}$ and $l = 17\, \text{cm}$ we have:

$$ \left( 4\, \text{cm} \right)^{2} + h^2 = \left( 17\, \text{cm} \right)^{2} $$ $$ h^2 = \left( 17\, \text{cm} \right)^{2} - \left( 4\, \text{cm} \right)^{2} $$ $$ h^2 = 289\, \text{cm}^2 - 16\, \text{cm}^2 $$ $$ h^2 = 273\, \text{cm}^2 $$ $$ h = \sqrt{ 273\, \text{cm}^2 } $$$$ h = \sqrt{ 273 }\, \text{cm} $$

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