Question
Find the slant height $ l $ of a cone if radius $r = 5\, \text{cm}$ and height $h = 11\, \text{cm}$.
Answer
$\sqrt{ 146 }\, \text{cm}$
Explanation
To find side $ l $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $r = 5\, \text{cm}$ and $h = 11\, \text{cm}$ we have:
$$ \left( 5\, \text{cm} \right)^{2} + \left( 11\, \text{cm} \right)^{2} = l^2 $$ $$ 25\, \text{cm}^2 + 121\, \text{cm}^2 = l^2 $$ $$ l^2 = 146\, \text{cm}^2 $$ $$ l = \sqrt{ 146\, \text{cm}^2 } $$$$ l = \sqrt{ 146 }\, \text{cm} $$This page was created using
Cone Calculator