Question

Find the area $A$ of a cone if height $h = 5 cm$ and slant height $l = 9.5 cm$ .

Answer

$141.9886 cm^{2}$

Explanation

STEP 1: find side $r$

To find side $r$ use Pythagorean Theorem:

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

After substituting $h = 5 cm$ and $l = 9.5 cm$ we have:

r^{2} + (5 cm)^{2} = (9.5 cm)^{2}

r^{2} = (9.5 cm)^{2} - (5 cm)^{2}

r^{2} = 90.25 cm^{2} - 25 cm^{2}

r^{2} = 65.25 cm^{2}

r = 65.25 cm^{2}

r = 8.0777 cm

STEP 2: find base area $A B$

To find base area $A B$ use formula:

A B = r^{2} \cdot π

After substituting $r = 8.0777 cm$ we have:

A B = (8.0777 cm)^{2} \cdot π

A B = 65.25 cm^{2} \cdot π

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 $r = 8.0777 cm$ and $l = 9.5 cm$ we have:

CS A = 9.5 cm \cdot 8.0777 cm \cdot π

CS A = 9.5 cm \cdot 8.0777 cm \cdot π

CS A = 76.7386 π cm^{2}

STEP 4: find area $A$

To find area $A$ use formula:

A = A B + CS A

After substituting $A B = 65.25 π cm^{2}$ and $CS A = 76.7386 π cm^{2}$ we have:

A = 65.25 π cm^{2} + 76.7386 π cm^{2}

A = 65.25 cm^{2} + 76.7386 cm^{2}

A = 141.9886 cm^{2}

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