Question
Find the volume $ V $ of a cone if diameter $d = 3\, \text{cm}$ and height $h = 6\, \text{cm}$.
Answer
$18\pi\, \text{cm}^3$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
$$ d = 2 \cdot r $$After substituting $d = 3\, \text{cm}$ we have:
$$ 3\, \text{cm} = 2 \cdot r $$ $$ r = \dfrac{ 3\, \text{cm} }{ 2 } $$ $$ r = \frac{ 3 }{ 2 }\, \text{cm} $$STEP 2: find volume $ V $
To find volume $ V $ use formula:
$$ V = \dfrac{ h ^{ 2 } \cdot r \cdot \pi}{ 3 } $$After substituting $r = \dfrac{ 3 }{ 2 }\, \text{cm}$ and $h = 6\, \text{cm}$ we have:
$$ V = \dfrac{ 36\, \text{cm}^2 \cdot \frac{ 3 }{ 2 }\, \text{cm} \cdot \pi}{ 3 }$$$$ V = \dfrac{ 54\, \text{cm}^3 \, \pi}{ 3 } $$$$ V = 18\pi\, \text{cm}^3 $$This page was created using
Cone Calculator