Question
Find the volume $ V $ of a cone if height $h = 5\, \text{cm}$ and base area $AB = 6\, \text{cm}$.
Answer
$11.5165\pi\, \text{cm}^2$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
After substituting $AB = 6\, \text{cm}$ we have:
$$ AB = r^2 \cdot \pi $$ $$ r^2 \cdot \pi = 6\, \text{cm} $$ $$ r = \sqrt{ \frac{ 6\, \text{cm} }{\pi} } $$ $$ r \approx 1.382 $$STEP 2: find volume $ V $
To find volume $ V $ use formula:
$$ V = \dfrac{ h ^{ 2 } \cdot r \cdot \pi}{ 3 } $$After substituting $r = 1.382\, \text{cm}^0$ and $h = 5\, \text{cm}$ we have:
$$ V = \dfrac{ 25\, \text{cm}^2 \cdot 1.382 \cdot \pi}{ 3 }$$$$ V = \dfrac{ 34.5494\, \text{cm}^2 \, \pi}{ 3 } $$$$ V = 11.5165\pi\, \text{cm}^2 $$This page was created using
Cone Calculator