Geometry

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- Arc Length Calculator
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- Center of Mass Calculator
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- Perimeter of a Circle
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- Perimeter of a Rhombus
- Perimeter of a Semicircle
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- Properties of a Parallelogram
- Pythagorean Theorem Calculator
- Side Angle Side Theorem
- Side Splitter Theorem
- Similar Triangles
- Special Right Triangles
- Surface Area of a Cone
- Surface Area of a Cube
- Surface Area of a Cylinder
- Surface Area of a Hemisphere
- Surface Area of a Pyramid
- Surface Area of a Sphere
- Surface Area of a Triangular Prism
- Triangle Inequality Theorem
- Types of Triangles
- Vertical Angles
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- Volume of a Cube
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Tutors/teachers:

Nikkolas

Tutor and Aerospace Engineer

# Surface Area of a Cone

## Cone Surface Area Formula

The formula for surface area of a cone is given as:

Where *SA* is the surface area, *h* is the height of the cone, and *r* is the radius of the circle at the cone’s base.

### Example Problems

**Problem 1:**

Find the surface area of a cone with a height of 6 and a radius of 4.

Solution:

1.) We have both required dimensions to use the surface area formula.

2.) Plugging the height and radius in, we get:

SA = πr[r + √(h^{2} + r^{2})]

SA = π(4)[4+ √(6^{2} + 4^{2})] = π(4)[11.2111] = 140.883

3.) **The surface area of the cone is 140.883.**

**Problem 2:**

Find the surface area of a cone with a height of 1 and a radius of 1.

Solution:

1.) We have both required dimensions to use the surface area formula.

2.) Plugging the height and radius in, we get:

SA = πr[r + √(h^{2} + r^{2})]

SA = π(1)[1+ √(1^{2} + 1^{2})] = π(1)[2.414] = 7.584

3.) **The surface area of the cone is 7.584.**

Result :

Worksheet 1

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Cheat sheet

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