Find the slant height $ l $ of a cone if radius $r = 15$ and area $A = 2449.2$.

$l = 36.9736$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 15 $ we have:

$$ AB = 15^2 \cdot \pi $$ $$ AB = 225 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 2449.2 $ and $ AB = 225\pi $ we have:

$$ 2449.2 = 225\pi + CSA $$ $$ CSA = 2449.2 - 225\pi $$ $$ CSA = 1742.3417 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 1742.3417 $ and $ r = 15 $ we have:

$$ 1742.3417 = 15 \cdot l \cdot \pi $$$$ l = \dfrac{ 1742.3417 }{ 15 \, \pi} $$$$ l = 36.9736 $$

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