Find the volume $ V $ of a cone if radius $r = 8$ and slant height $l = 17$.
Answer
$V = 320\pi$
Explanation
STEP 1: find side $ h $
To find side $ h $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $ r = 8 $ and $ l = 17 $ we have:
$$ 8^2 + h^2 = 17^2 $$ $$ h^2 = 17^2 - 8^2 $$ $$ h^2 = 289 - 64 $$ $$ h^2 = 225 $$ $$ h = \sqrt{ 225 } $$$$ h = 15 $$STEP 2: find volume $ V $
To find volume $ V $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ r = 8 $ and $ h = 15 $ we have:
$$ V = \dfrac{ 64 \cdot 15 \cdot \pi}{ 3 }$$$$ V = \dfrac{ 960 \, \pi}{ 3 } $$$$ V = 320\pi $$This page was created using
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