Find the slant height $l$ of a cone if radius $r = 4 cm$ and area $A = 251.2 cm$ .

Answer

$15.9898$

Explanation

STEP 1: find base area $A B$

To find base area $A B$ use formula:

A B = r^{2} \cdot π

After substituting $r = 4 cm$ we have:

A B = (4 cm)^{2} \cdot π

A B = 16 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 $A = 251.2 cm$ and $A B = 16 π cm^{2}$ we have:

251.2 cm = 16 π cm^{2} + CS A

CS A = 251.2 cm - 16 π cm^{2}

CS A = 200.9345 cm

STEP 3: find slant height $l$

To find slant height $l$ use formula:

CS A = l \cdot r \cdot π

After substituting $CS A = 200.9345 cm$ and $r = 4 cm$ we have:

200.9345 cm = 4 cm \cdot l \cdot π

l = \frac{200.9345 cm}{4 cm π}

l \approx 15.9898

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Find the slant height l of a cone if radius r=4cm and area A=251.2cm.

15.9898

Find the slant height $l$ of a cone if radius $r = 4 cm$ and area $A = 251.2 cm$ .

$15.9898$