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More Geometry Lessons

Geometry Worksheets

In these lessons, we will learn

** Surface Area of a Cone **

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

**How to find the surface area of a cone when the slant height is given?**

Example:

Find the surface area. r = 9cm, h = 12cm, l = 15cm. (Leave answer in π form) 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.

Example:

Find the surface area. r = 7cm, h = 24cm. (Leave answer in π form)**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.

### 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.
**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.

More Geometry Lessons

Geometry Worksheets

In these lessons, we will learn

- 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.

A cone is a solid with a circular **base**. 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

= πrs + πr^{2}

= πr(r + s)

Example:

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

Solution:

Area = πr(r + s)

=

= 1,257.14 cm^{2}

Example:

Find the surface area. r = 9cm, h = 12cm, l = 15cm. (Leave answer in π form) Example:

What is the surface area of the cone? Round the answer to the nearest hundredth.

Example:

Find the surface area. r = 7cm, h = 24cm. (Leave answer in π form)

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.

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