Find the slant height $ l $ of a cone if radius $r = 2$ and area $A = 37.68$.

$l = 3.997$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

$$ AB = r^2 \cdot \pi $$

After substituting $ r = 2 $ we have:

$$ AB = 2^2 \cdot \pi $$ $$ AB = 4 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 37.68 $ and $ AB = 4\pi $ we have:

$$ 37.68 = 4\pi + CSA $$ $$ CSA = 37.68 - 4\pi $$ $$ CSA = 25.1136 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

$$ CSA = r \cdot l \cdot \pi $$

After substituting $ CSA = 25.1136 $ and $ r = 2 $ we have:

$$ 25.1136 = 2 \cdot l \cdot \pi $$$$ l = \dfrac{ 25.1136 }{ 2 \, \pi} $$$$ l = 3.997 $$

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