Question

Find the area $A$ of a cone if diameter $d = 18 cm$ and height $h = 12 cm$ .

Answer

$216 π cm^{2}$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

d = 2 \cdot r

After substituting $d = 18 cm$ we have:

18 cm = 2 \cdot r

r = \frac{18 cm}{2}

r = 9 cm

STEP 2: find base area $A B$

To find base area $A B$ use formula:

A B = r^{2} \cdot π

After substituting $r = 9 cm$ we have:

A B = (9 cm)^{2} \cdot π

A B = 81 cm^{2} \cdot π

STEP 3: find side $l$

To find side $l$ use Pythagorean Theorem:

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

After substituting $r = 9 cm$ and $h = 12 cm$ we have:

(9 cm)^{2} + (12 cm)^{2} = l^{2}

81 cm^{2} + 144 cm^{2} = l^{2}

l^{2} = 225 cm^{2}

l = 225 cm^{2}

l = 15 cm

STEP 4: find Curved Surface Area $CS A$

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

CS A = l \cdot r \cdot π

After substituting $r = 9 cm$ and $l = 15 cm$ we have:

CS A = 15 cm \cdot 9 cm \cdot π

CS A = 15 cm \cdot 9 cm \cdot π

CS A = 135 π cm^{2}

STEP 5: find area $A$

To find area $A$ use formula:

A = A B + CS A

After substituting $A B = 81 π cm^{2}$ and $CS A = 135 π cm^{2}$ we have:

A = 81 π cm^{2} + 135 π cm^{2}

A = 81 π cm^{2} + 135 π cm^{2}

A = 216 π cm^{2}

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