Question
Find the height $ h $ of a cone if radius $r = 9\, \text{cm}$ and slant height $l = 9\, \text{cm}$.
Answer
Problem has no solutions.
Explanation
To find side $ h $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $r = 9\, \text{cm}$ and $l = 9\, \text{cm}$ we have:
$$ \left( 9\, \text{cm} \right)^{2} + h^2 = \left( 9\, \text{cm} \right)^{2} $$ $$ h^2 = \left( 9\, \text{cm} \right)^{2} - \left( 9\, \text{cm} \right)^{2} $$ $$ h^2 = 81\, \text{cm}^2 - 81\, \text{cm}^2 $$ $$ h^2 = $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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