Question
Find the height $ h $ of a cone if radius $r = 5\, \text{cm}$ and slant height $l = 5 \sqrt{ 2 }\, \text{cm}$.
Answer
$5\, \text{cm}$
Explanation
To find side $ h $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $r = 5\, \text{cm}$ and $l = 5 \sqrt{ 2 }\, \text{cm}$ we have:
$$ \left( 5\, \text{cm} \right)^{2} + h^2 = \left( 5 \sqrt{ 2 }\, \text{cm} \right)^{2} $$ $$ h^2 = \left( 5 \sqrt{ 2 }\, \text{cm} \right)^{2} - \left( 5\, \text{cm} \right)^{2} $$ $$ h^2 = 50\, \text{cm}^2 - 25\, \text{cm}^2 $$ $$ h^2 = 25\, \text{cm}^2 $$ $$ h = \sqrt{ 25\, \text{cm}^2 } $$$$ h = 5\, \text{cm} $$This page was created using
Cone Calculator