Find the slant height $l$ of a cone if radius $r = 24.2 cm$ and area $A = 4802.4416 cm$ .

Answer

$55.4647$

Explanation

STEP 1: find base area $A B$

To find base area $A B$ use formula:

A B = r^{2} \cdot π

After substituting $r = 24.2 cm$ we have:

A B = (24.2 cm)^{2} \cdot π

A B = 585.64 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 $A = 4802.4416 cm$ and $A B = 585.64 π cm^{2}$ we have:

4802.4416 cm = 585.64 π cm^{2} + CS A

CS A = 4802.4416 cm - 585.64 cm^{2}

CS A = 4216.8016 cm

STEP 3: find slant height $l$

To find slant height $l$ use formula:

CS A = l \cdot r \cdot π

After substituting $CS A = 4216.8016 cm$ and $r = 24.2 cm$ we have:

4216.8016 cm = 24.2 cm \cdot l \cdot π

l = \frac{4216.8016 cm}{24.2 cm π}

l \approx 55.4647

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Find the slant height l of a cone if radius r=24.2cm and area A=4802.4416cm.

55.4647

Find the slant height $l$ of a cone if radius $r = 24.2 cm$ and area $A = 4802.4416 cm$ .

$55.4647$