Find the slant height $ s $ of a pyramid if height $h = 10.6$ and base radius $r = 9.3$.
Answer
$s = 14.1014$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ a }{ 2 } $$After substituting $ r = 9.3 $ we have:
$$ 9.3 = \dfrac{ a }{ 2 } $$ $$ a = 9.3 \cdot 2 $$ $$ a = 18.6 $$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 = 10.6 $ and $ a = 18.6 $ we have:
$$ 10.6^2 + \frac{ 18.6^2 }{ 4 }= s^2 $$ $$ 112.36 + \frac{ 345.96 }{ 4 }= s^2 $$ $$ 112.36 + 86.49 = s^2 $$ $$ s^2 = 198.85 $$ $$ s = \sqrt{ 198.85 } $$$$ s = 14.1014 $$This page was created using
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