Find the slant height $ s $ of a pyramid if height $h = 4$ and base radius $r = 60$.
Answer
$s = 4 \sqrt{ 226 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ a }{ 2 } $$After substituting $ r = 60 $ we have:
$$ 60 = \dfrac{ a }{ 2 } $$ $$ a = 60 \cdot 2 $$ $$ a = 120 $$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 = 4 $ and $ a = 120 $ we have:
$$ 4^2 + \frac{ 120^2 }{ 4 }= s^2 $$ $$ 16 + \frac{ 14400 }{ 4 }= s^2 $$ $$ 16 + 3600 = s^2 $$ $$ s^2 = 3616 $$ $$ s = \sqrt{ 3616 } $$$$ s = 4 \sqrt{ 226 } $$This page was created using
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