# Surface Area of a Cone Formula

A geometric object with a smooth transition from a flat base to the apex or vertex is called a cone. It consists of segments, split lines, or lines that link a commonality, the pinnacle, to most of the spots on a base that are not in the same plane as the apex.

**Surface Area of Cone**

The surface area of a cone is the area filled by the outer edge of a cone. It is usually expressed in terms of square units. The form of a cone is created by stacking numerous triangles and spinning them around an axis. It has a total surface area as well as a curved surface area because it has a flat base. A cone can be classified as either a right circular or an oblique cone. In a right circular cone, the vertex is normally vertically above the centre of the base, but in an oblique cone, the vertex is not vertically above the centre of the base.

**Formula**

TSA = Ï€r(r + l) or Ï€r(r + âˆš(r^{2}+ h^{2}))where h denotes the height of the cone and r is the radius and l is the slant height.

**Derivation**

Assume a cone of height, radius and slant height h, r and l respectively.

Cut it from the center so it is converted into a 2D shape.

TSA of cone = CSA + base area

= Ï€r

^{2}+ Ï€rl= Ï€r (r + l)

Hence proved.

**Sample Problems**

**Problem 1. Find the TSA of a cone if its radius and slant height are 4 cm and 5 cm.**

**Solution:**

Given: r = 4 cm

l = 5 cm

TSA = Ï€r (r + l)

= 3.14 x 4(4 + 5)

= 113.04 cm

^{2}

**Problem 2. Find the TSA of a cone if its slant height is 8 cm and radius is 2 cm.**

**Solution:**

Given: r = 2 cm

l = 8 cm

TSA = Ï€r (r + l)

= 3.14 x 2(2 + 8)

= 62.8 cm

^{2}

**Problem 3. Find the slant height of a cone if its TSA is 616 cm ^{2} and radius 7 cm.**

**Solution:**

Given: TSA = 616 cm

^{2}r = 7 cm

Let the slant height be l cm.

Since TSA of a cone = Ï€r (r + l)

â‡’ 616 = 22x7x (7 + l)/7

â‡’ 7 + l = 616/22

l = 28 – 7

l = 21 cm

**Problem 4. Find the TSA of a cone with a radius of 14 cm and slant height of 8 cm.**

**Solution:**

Given: r = 14 cm

l = 8 cm

TSA = Ï€r (r + l)

= 3.14 x 14(14 + 8)

= 967.12 cm

^{2}

**Problem 5. Find the TSA of a cone with a radius of 5 cm and slant height of 8 cm.**

**Solution:**

Given: r = 5 cm

l = 8 cm

TSA = Ï€r (r + l)

= 3.14 x 5(5 + 8)

= 204.10 cm

^{2}

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