Find the volume $ V $ of a pyramid if height $h = 2$ and lateral edge $e = 1$.
Answer
Problem has no solutions.
Explanation
To find base diagonal $ d $ use Pythagorean Theorem:
$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$After substituting $ h = 2 $ and $ e = 1 $ we have:
$$ 2^2 + \frac{ d^2 }{ 4 } = 1^2 $$ $$ \frac{ d^2 }{ 4 } = 1^2 - 2^2 $$ $$ \frac{ d^2 }{ 4 } = 1 - 4 $$ $$ d^2 = -3 \cdot 4 $$ $$ d^2 = -12 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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