Question
Find the slant height $ l $ of a cone if base area $AB = 78.5\, \text{cm}$ and Curved Surface Area $CSA = 188.4\, \text{cm}$.
Answer
$11.9969\, \text{cm}$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
After substituting $AB = 78.5\, \text{cm}$ we have:
$$ AB = r^2 \cdot \pi $$ $$ r^2 \cdot \pi = 78.5\, \text{cm} $$ $$ r = \sqrt{ \frac{ 78.5\, \text{cm} }{\pi} } $$ $$ r \approx 4.9987 $$STEP 2: find slant height $ l $
To find slant height $ l $ use formula:
$$ CSA = l \cdot r \cdot \pi$$After substituting $CSA = 188.4\, \text{cm}$ and $r = 4.9987\, \text{cm}^0$ we have:
$$ 188.4\, \text{cm} = 4.9987 \cdot l \cdot \pi $$$$ l = \dfrac{ 188.4\, \text{cm}}{ 4.9987 \, \pi } $$$$ l \approx 11.9969\, \text{cm} $$This page was created using
Cone Calculator