Find the volume $ V $ of a pyramid if height $h = 16$ and slant height $s = 20$.
Answer
$V = 3072$
Explanation
STEP 1: find side $ a $
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 16 $ and $ s = 20 $ we have:
$$ 16^2 + \frac{ a^2 }{ 4 } = 20^2 $$ $$ \frac{ a^2 }{ 4 } = 20^2 - 16^2 $$ $$ \frac{ a^2 }{ 4 } = 400 - 256 $$ $$ a^2 = 144 \cdot 4 $$ $$ a^2 = 576 $$ $$ a = \sqrt{ 576 } $$$$ a = 24 $$STEP 2: find volume $ V $
To find volume $ V $ use formula:
$$ V = \dfrac{ a ^{ 2 } \cdot h }{ 3 } $$After substituting $ a = 24 $ and $ h = 16 $ we have:
$$ V = \dfrac{ 576 \cdot 16 }{ 3 }$$$$ V = \dfrac{ 9216 }{ 3 } $$$$ V = 3072 $$This page was created using
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