Question

Find the area $A$ of a cone if radius $r = 1.21 cm$ and height $h = 3.8 cm$ .

Answer

$6.2896 cm^{2}$

Explanation

STEP 1: find base area $A B$

To find base area $A B$ use formula:

A B = r^{2} \cdot π

After substituting $r = 1.21 cm$ we have:

A B = (1.21 cm)^{2} \cdot π

A B = 1.4641 cm^{2} \cdot π

STEP 2: find side $l$

To find side $l$ use Pythagorean Theorem:

r^{2} + h^{2} = l^{2}

After substituting $r = 1.21 cm$ and $h = 3.8 cm$ we have:

(1.21 cm)^{2} + (3.8 cm)^{2} = l^{2}

1.4641 cm^{2} + 14.44 cm^{2} = l^{2}

l^{2} = 15.9041 cm^{2}

l = 15.9041 cm^{2}

l = 3.988 cm

STEP 3: find Curved Surface Area $CS A$

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

CS A = l \cdot r \cdot π

After substituting $r = 1.21 cm$ and $l = 3.988 cm$ we have:

CS A = 3.988 cm \cdot 1.21 cm \cdot π

CS A = 3.988 cm \cdot 1.21 cm \cdot π

CS A = 4.8255 π cm^{2}

STEP 4: find area $A$

To find area $A$ use formula:

A = A B + CS A

After substituting $A B = 1.4641 π cm^{2}$ and $CS A = 4.8255 π cm^{2}$ we have:

A = 1.4641 π cm^{2} + 4.8255 π cm^{2}

A = 1.4641 cm^{2} + 4.8255 cm^{2}

A = 6.2896 cm^{2}

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