Math Education

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Surface Area of a Cone: Formula & Examples

Published: 11.07.2026·Updated: 22.07.2026

Dewi Lestari

Mathematics Specialist

Surface Area of a Cone: Formula & Examples

The surface area of a cone is A = π × r × (r + s) (πr(r+s)), where r is the base radius and s is the slant height. For the lateral surface only, use A = πrs. Quick example: a cone with r = 7 cm and s = 25 cm has a surface area of (22/7) × 7 × (7 + 25) = 704 cm².

A cone has a circular base (πr²) and a lateral surface (πrs). s = slant height.

How to Calculate the Surface Area of a Cone + Worked Example

A cone consists of one circular base (πr²) and a lateral surface shaped like a sector (πrs). The slant height s is found with the Pythagorean theorem: s = √(r² + t²), where t is the height of the cone.

Worked example: A birthday hat shaped like a cone has a radius of 7 cm and a height of 24 cm. What is its total surface area? (π = 22/7)

Step 1: r = 7, t = 24 → s = √(7² + 24²) = √(49 + 576) = √625 = 25 cm. Step 2: A = πr(r + s) = (22/7) × 7 × (7 + 25). Step 3: A = 22 × 32 = 704 cm².

Why It Matters

The surface area of a cone is taught in Grade 9 (curved solids) and is often tested in standardised exams. The concept is used to estimate material for cone hats, funnels, ice-cream cones, and tower roofs. This topic is special because it combines the circle and the Pythagorean theorem in a single problem.

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Lateral Surface Area of a Cone

The lateral surface area of a cone — the curved part without the base — is calculated with the formula A = π × r × s, where r is the base radius and s is the slant height. For example, a cone with a radius of 7 cm and a slant height of 10 cm has a lateral surface area of 3.14 × 7 × 10 = 219.8 cm². The lateral surface area is different from the total surface area, because the total surface area adds the area of the circular base (π × r²) to the lateral surface area.

Want to understand solids with a mentor? Try a free class at Algonova or see the Algonova mathematics programme. Learn also The Volume of a Cone Formula and Surface Area of a Sphere.

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Algonova Indonesia math classes come in three formats: 1-on-1 private, a mini-group of 2–4 kids, and a group of up to 10 students with similar ability and school grade levels. This small group format is deliberately chosen because it provides the optimal balance between social interaction with peers and personal teacher attention. In a mini-group, every child averages about 10 minutes of direct teacher interaction in a single session. Compare with traditional offline bimbel typically of 20-40 students per class — direct interaction there is only 1-2 minutes per child, or none at all. For families wanting full attention, one-on-one private class format is also available with one student per teacher. This format is more intensive and suits competition preparation, catching up from severe gaps, or specific topic depth.

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What is the formula for the surface area of a cone?

The surface area of a cone is A = πr(r + s), where r is the base radius and s is the slant height. For the lateral surface only, use A = πrs.

What is the slant height (s) of a cone?

The slant height is the distance from the apex of the cone to the edge of its base. It is calculated with the Pythagorean theorem: s = √(r² + t²), where t is the height of the cone.

How do you calculate the surface area of a cone?

First find the slant height s if it is not given (s = √(r² + t²)), then substitute into A = πr(r + s). Example: r=7, s=25 → (22/7)×7×32 = 704 cm².

In which grade is the surface area of a cone taught?

The surface area of a cone is taught in Grade 9 within the chapter on curved solids, alongside cylinders and spheres.

Other Solids & Math Topics

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