Find the slant height $ l $ of a cone if radius $r = 10$ and area $A = 1413$.

$l = 34.9772$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 10 $ we have:

$$ AB = 10^2 \cdot \pi $$ $$ AB = 100 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 1413 $ and $ AB = 100\pi $ we have:

$$ 1413 = 100\pi + CSA $$ $$ CSA = 1413 - 100\pi $$ $$ CSA = 1098.8407 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 1098.8407 $ and $ r = 10 $ we have:

$$ 1098.8407 = 10 \cdot l \cdot \pi $$$$ l = \dfrac{ 1098.8407 }{ 10 \, \pi} $$$$ l = 34.9772 $$

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