The image above is a cone.

To compute the area of a cone, two essential parameters is needed and this parameters are the radius of the cone (r) and the slant height of the cone (h).

The formula for calculating the area of a cone:

A = πrl + πr²

Where;

**A** = Area of the Cone

r = Radius of the Cone

Let’s solve an example:

Find the area of a cone when the radius of the cone is 9 cm and the slant height of the cone is 12 cm.

This implies that;

r = Radius of the cone = 9 cm

l = Slant height of the cone = 12 cm

A = πrl + πr²

A = 3.142 x 9 x 12 + 3.142 x 9²

A = 339.336 + 254.502

A = 593.83

Therefore, the **area of the cone** is **593.83 cm².**

**Calculating the Area of a cone using Diameter and Slant height of the cone.**

A = ^{πdl} / _{2} + ^{πd}^{2} / _{4}

Where;

d = Diameter of the Cone

l = Slant height of the Cone

Let’s solve an example:

Find the area of a cone when the diameter of the cone is 18 cm and the slant height of the cone is 22 cm?

This implies that;

d = diameter of the cone = 18 cm

l = Slant height of the cone = 22 cm

A = ^{πdl} / _{2} + ^{πd}^{2} / _{4}

A = ^{3.142 x 18 x 22} / _{2} + ^{3.142 (18)}^{2} / _{4}

A = ^{1244.232} / _{2} + ^{1018.008} / _{4}

A = 622.116 + 254.502

A = 876.6

Therefore, the **area of the cone** with diameter is **876.6 cm ^{2}.**

**Calculating the Slant height of a cone using Radius of the cone and Area of the cone.**

l = ^{A – πr}^{2} / _{πr}

Where;

A = Area of the Cone

r = Radius of the Cone

Let’s solve an example:

Find the slant height of a cone when the radius of the cone is 8 cm and the area of the cone is 220 cm^{2}.

This implies that;

A = Area of the cone = 220 cm^{2}

r = Radius of the cone = 8 cm

l = ^{A – πr}^{2} / _{πr}

l = ^{220 – 3.142 x 8}^{2} / _{3.142 x 8}

l = ^{220 – 3.142 x 64} / _{25.136}

l = ^{220 – 201.088} / _{25.136}

l = ^{18.91} / _{25.136}

l = 0.75

Therefore, the **slant height of the cone** with radius is **0.75 cm.**