Find the volume $ V $ of a cone if radius $r = 7.8$ and slant height $l = 10$.
Answer
$V = 126.9081\pi$
Explanation
STEP 1: find side $ h $
To find side $ h $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $ r = 7.8 $ and $ l = 10 $ we have:
$$ 7.8^2 + h^2 = 10^2 $$ $$ h^2 = 10^2 - 7.8^2 $$ $$ h^2 = 100 - 60.84 $$ $$ h^2 = 39.16 $$ $$ h = \sqrt{ 39.16 } $$$$ h = 6.2578 $$STEP 2: find volume $ V $
To find volume $ V $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ r = 7.8 $ and $ h = 6.2578 $ we have:
$$ V = \dfrac{ 60.84 \cdot 6.2578 \cdot \pi}{ 3 }$$$$ V = \dfrac{ 380.7243 \, \pi}{ 3 } $$$$ V = 126.9081\pi $$This page was created using
Cone Calculator