Find the volume $ V $ of a cone if radius $r = 3$ and area $A = 24$.
Answer
Problem has no solutions.
Explanation
STEP 1: find base area $ AB $
To find base area $ AB $ use formula:
$$ AB = r^2 \cdot \pi $$After substituting $ r = 3 $ we have:
$$ AB = 3^2 \cdot \pi $$ $$ AB = 9 \cdot \pi $$STEP 2: find Curved Surface Area $ CSA $
To find Curved Surface Area $ CSA $ use formula:
$$ A = AB + CSA $$After substituting $ A = 24 $ and $ AB = 9\pi $ we have:
$$ 24 = 9\pi + CSA $$ $$ CSA = 24 - 9\pi $$ $$ CSA = -4.2743 $$The result has to be greater than zero. $ \Longrightarrow $ The problem has no solution.
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