Question
Find the volume $ V $ of a cone if height $h = 14.7\, \text{cm}$ and base area $AB = 13\, \text{cm}$.
Answer
$146.5243\pi\, \text{cm}^2$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
After substituting $AB = 13\, \text{cm}$ we have:
$$ AB = r^2 \cdot \pi $$ $$ r^2 \cdot \pi = 13\, \text{cm} $$ $$ r = \sqrt{ \frac{ 13\, \text{cm} }{\pi} } $$ $$ r \approx 2.0342 $$STEP 2: find volume $ V $
To find volume $ V $ use formula:
$$ V = \dfrac{ h ^{ 2 } \cdot r \cdot \pi}{ 3 } $$After substituting $r = 2.0342\, \text{cm}^0$ and $h = 14.7\, \text{cm}$ we have:
$$ V = \dfrac{ 216.09\, \text{cm}^2 \cdot 2.0342 \cdot \pi}{ 3 }$$$$ V = \dfrac{ 439.5729\, \text{cm}^2 \, \pi}{ 3 } $$$$ V = 146.5243\pi\, \text{cm}^2 $$This page was created using
Cone Calculator