Question

Find the area $A$ of a cone if radius $r = 6.1 cm$ and height $h = 18.1 cm$ .

Answer

$153.7216 cm^{2}$

Explanation

STEP 1: find base area $A B$

To find base area $A B$ use formula:

A B = r^{2} \cdot π

After substituting $r = 6.1 cm$ we have:

A B = (6.1 cm)^{2} \cdot π

A B = 37.21 cm^{2} \cdot π

STEP 2: find side $l$

To find side $l$ use Pythagorean Theorem:

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

After substituting $r = 6.1 cm$ and $h = 18.1 cm$ we have:

(6.1 cm)^{2} + (18.1 cm)^{2} = l^{2}

37.21 cm^{2} + 327.61 cm^{2} = l^{2}

l^{2} = 364.82 cm^{2}

l = 364.82 cm^{2}

l = 19.1003 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 $r = 6.1 cm$ and $l = 19.1003 cm$ we have:

CS A = 19.1003 cm \cdot 6.1 cm \cdot π

CS A = 19.1003 cm \cdot 6.1 cm \cdot π

CS A = 116.5116 π cm^{2}

STEP 4: find area $A$

To find area $A$ use formula:

A = A B + CS A

After substituting $A B = 37.21 π cm^{2}$ and $CS A = 116.5116 π cm^{2}$ we have:

A = 37.21 π cm^{2} + 116.5116 π cm^{2}

A = 37.21 cm^{2} + 116.5116 cm^{2}

A = 153.7216 cm^{2}

This page was created using

Cone Calculator