Question
Find the slant height $ l $ of a cone if radius $r = 3\, \text{cm}$ and height $h = 6\, \text{cm}$.
Answer
$3 \sqrt{ 5 }\, \text{cm}$
Explanation
To find side $ l $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $r = 3\, \text{cm}$ and $h = 6\, \text{cm}$ we have:
$$ \left( 3\, \text{cm} \right)^{2} + \left( 6\, \text{cm} \right)^{2} = l^2 $$ $$ 9\, \text{cm}^2 + 36\, \text{cm}^2 = l^2 $$ $$ l^2 = 45\, \text{cm}^2 $$ $$ l = \sqrt{ 45\, \text{cm}^2 } $$$$ l = 3 \sqrt{ 5 }\, \text{cm} $$This page was created using
Cone Calculator