Find the slant height $ s $ of a pyramid if height $h = 12$ and base radius $r = 10$.
Answer
$s = 2 \sqrt{ 61 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ a }{ 2 } $$After substituting $ r = 10 $ we have:
$$ 10 = \dfrac{ a }{ 2 } $$ $$ a = 10 \cdot 2 $$ $$ a = 20 $$STEP 2: find slant height $ s $
To find slant height $ s $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 12 $ and $ a = 20 $ we have:
$$ 12^2 + \frac{ 20^2 }{ 4 }= s^2 $$ $$ 144 + \frac{ 400 }{ 4 }= s^2 $$ $$ 144 + 100 = s^2 $$ $$ s^2 = 244 $$ $$ s = \sqrt{ 244 } $$$$ s = 2 \sqrt{ 61 } $$This page was created using
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