Find the slant height $ l $ of a cone if radius $r = 11$ and area $A = 1070.74$.

$l = 19.9843$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 11 $ we have:

$$ AB = 11^2 \cdot \pi $$ $$ AB = 121 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ A = AB + CSA $$

After substituting $ A = 1070.74 $ and $ AB = 121\pi $ we have:

$$ 1070.74 = 121\pi + CSA $$ $$ CSA = 1070.74 - 121\pi $$ $$ CSA = 690.6073 $$

STEP 3: find slant height $ l $

To find slant height $ l $ use formula:

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

After substituting $ CSA = 690.6073 $ and $ r = 11 $ we have:

$$ 690.6073 = 11 \cdot l \cdot \pi $$$$ l = \dfrac{ 690.6073 }{ 11 \, \pi} $$$$ l = 19.9843 $$

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