Find the slant height $ s $ of a pyramid if height $h = 4$ and base radius $r = 3$.
Answer
$s = 5$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ a }{ 2 } $$After substituting $ r = 3 $ we have:
$$ 3 = \dfrac{ a }{ 2 } $$ $$ a = 3 \cdot 2 $$ $$ a = 6 $$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 = 4 $ and $ a = 6 $ we have:
$$ 4^2 + \frac{ 6^2 }{ 4 }= s^2 $$ $$ 16 + \frac{ 36 }{ 4 }= s^2 $$ $$ 16 + 9 = s^2 $$ $$ s^2 = 25 $$ $$ s = \sqrt{ 25 } $$$$ s = 5 $$This page was created using
Pyramid Calculator