In these lessons, we will learn

Related Topics: More Geometry Lessons, Geometry Worksheets

** Surface Area of a Cone **

### Surface area of a cone when given the slant height

The following video shows how to find the surface area of a cone when the slant height is given.
Example: What is the surface area of the cone? Round the answer to the nearest hundredth.

### Surface area of cone when not given the slant height

The following video shows how to find the surface area of a cone when not given the slant height.
How to calculate the surface area of a cone when the slant height is not given.

The Pythagorean Theorem will be used to calculate the slant height using the radius and height of the cone as the right triangle's legs.

### Word Problems about cones

Example 1: A cone-shaped roof has a diameter of 12 ft. and a height of 8 ft. If roofing material comes in 120 square-foot rolls, how many rolls will be needed to cover this roof?

Example 2: The height of the Pyramid of Menkaure is 216 ft and the side of the (square) base measures 346 ft. Find the lateral surface area.
Find the surface area of a composite figure that consists of two cones and a cylinder.

### Derive the formula for the surface area of a cone

This video shows the derivation of the formula for the Surface Area of a Cone.
This video shows how to derive the formula for the surface area of a cone.

In this lesson, we'll take a cone, slice it, squash it, dissect it, and figure out a formula for its surface area.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

- how to calculate the surface area of a cone when given the slant height.
- how to calculate the surface area of a cone when not given the slant height.
- how to solve word problems about cones.
- how to derive the formula for the surface area of a cone.

Related Topics: More Geometry Lessons, Geometry Worksheets

A cone is a solid with a circular **bas****e**. It has a **curved surface** which tapers (i.e. decreases in size) to a **vertex ** at the top. The **height **of the cone is the perpendicular distance from the base to the vertex.

The net of a solid **cone** consists of a small circle and a sector of a larger circle. The arc of the sector has the same length as the circumference of the smaller circle.

Surface area of cone = Area of sector + area of circle

Example:

A cone has a circular base of radius 10 cm and a slant height of 30 cm. Calculate the surface area.

Solution:

Area = π*r*(*r* + *s*)

=

= 1,257.14 cm^{2}

The Pythagorean Theorem will be used to calculate the slant height using the radius and height of the cone as the right triangle's legs.

Example 2: The height of the Pyramid of Menkaure is 216 ft and the side of the (square) base measures 346 ft. Find the lateral surface area.

In this lesson, we'll take a cone, slice it, squash it, dissect it, and figure out a formula for its surface area.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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