Math Education

5 min read

Surface Area of a Cone: Formula & Examples

Published: 11.07.2026·Updated: 11.07.2026

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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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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