Find the slant height $l$ of a cone if radius $r = 13.7 cm$ and area $A = 1793.8506 cm$ .

Answer

$37.3179$

Explanation

STEP 1: find base area $A B$

To find base area $A B$ use formula:

A B = r^{2} \cdot π

After substituting $r = 13.7 cm$ we have:

A B = (13.7 cm)^{2} \cdot π

A B = 187.69 cm^{2} \cdot π

STEP 2: find Curved Surface Area $CS A$

To find Curved Surface Area $CS A$ use formula:

A = A B + CS A

After substituting $A = 1793.8506 cm$ and $A B = 187.69 π cm^{2}$ we have:

1793.8506 cm = 187.69 π cm^{2} + CS A

CS A = 1793.8506 cm - 187.69 cm^{2}

CS A = 1606.1606 cm

STEP 3: find slant height $l$

To find slant height $l$ use formula:

CS A = l \cdot r \cdot π

After substituting $CS A = 1606.1606 cm$ and $r = 13.7 cm$ we have:

1606.1606 cm = 13.7 cm \cdot l \cdot π

l = \frac{1606.1606 cm}{13.7 cm π}

l \approx 37.3179

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Find the slant height l of a cone if radius r=13.7cm and area A=1793.8506cm.

37.3179

Find the slant height $l$ of a cone if radius $r = 13.7 cm$ and area $A = 1793.8506 cm$ .

$37.3179$