Question
Find the height $ h $ of a cone if radius $r = 6\, \text{cm}$ and slant height $l = 10\, \text{cm}$.
Answer
$8\, \text{cm}$
Explanation
To find side $ h $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $r = 6\, \text{cm}$ and $l = 10\, \text{cm}$ we have:
$$ \left( 6\, \text{cm} \right)^{2} + h^2 = \left( 10\, \text{cm} \right)^{2} $$ $$ h^2 = \left( 10\, \text{cm} \right)^{2} - \left( 6\, \text{cm} \right)^{2} $$ $$ h^2 = 100\, \text{cm}^2 - 36\, \text{cm}^2 $$ $$ h^2 = 64\, \text{cm}^2 $$ $$ h = \sqrt{ 64\, \text{cm}^2 } $$$$ h = 8\, \text{cm} $$This page was created using
Cone Calculator