  # Surface Area of a Cone

In this worksheet, students will learn the formula for finding the surface area of a cone and be able to apply it. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Volume and Surface Area Calculations

Difficulty level:   #### Worksheet Overview

Where is the best place to store ice cream cones? Conetainers....... Sorry, that's the best I could do! Now if you are like me, you buy something first and worry about wrapping it up later.

You don't think about how awkward a shape is until you have to wrap it.

Cone shapes are awkward.  To buy the correct amount of wrapping paper we first need to know the surface area.

To find the surface area, we need a formula.

First, there is some key information that you need to be aware of.

You will need to work with a slanted height shown as in the formula.

You will need to work with value of 3.142 or 3.14 can be used.

For these types of questions using a scientific calculator is best as the value of is decided for you.

You need to work with the radius, which is the distance from the centre of a circle to the edge.

Area is always measured in units² Nay bother.

The formula comes in three stages:

1.  To find the area of the curved face the formula is x r x l

2. To find the area of the base the formula is x r² x r x l  x r²

It can be a bother having to learn so many formulas, but let us look at this closely.

A cone has a circular shape so the formula for finding an area of a circle is in it. x r²

This gives us the area of the surface of the base.

The other part of the formula starts the same, uses the radius, so the only other thing to think about is selecting (l) the slant height.

Question setters often give a vertical and a slant height, so beware.  Think that a cone slants. That is how I remember!

Let's get started, I bet you can't conetain yourself! Find the surface area of this cone.  The radius is 4 cm. The slant height is 7 cm.

Part 1 x r x l x 4 x 7 = 87.96 cm²

Part 2 x r x r x 4 x 4 = 50.27 cm²

Part 3

87.96 + 50.27 = 138.23 cm²

Just beware of a few things to look out for.

Sometimes you are given the diameter of the cone, remember to halve it to get the radius.

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