Surface Area (Edexcel IGCSE Maths A (Modular))

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Written by: Naomi C

Reviewed by: Dan Finlay

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Surface Area

What is surface area?

The surface area of a 3D object is the sum of the areas of all the faces that make up the shape
- Area is a 2D idea being applied into a 3D situation
- A face is one of the flat or curved surfaces that make up a 3D object

How do I find the surface area of cubes, cuboids, and prisms?

In cubes, cuboids, and polygonal-based prisms (prisms whose bases have straight sides), all the faces are flat
The surface area is found by
- calculating the area of each individual flat face
- adding these areas together
You should remember the formulas for the area of a rectangle, a triangle, and a circle to help you calculate surface areas
When calculating surface area, it can be helpful to draw a 2D net for the 3D shape in question

How do I find the surface area of a cylinder?

A cylinder has two flat surfaces (the top and the base) and one curved surface
The net of a cylinder consists of two circles and a rectangle
The curved surface area of a cylinder, A, with base radius, r, and height, h, is therefore given by
- $A = 2 π r h$
- This formula is given to you in the exam
The total surface area of a cylinder, A_Total, can be found using the formula
- $A_{T o t a l} = 2 π r h + 2 π r^{2}$
- This formula is not given to you in the exam

How do I find the surface area of a cone?

A cone has one flat surface (the base) and one curved surface
The net of a cone, with radius, r, perpendicular height, h, and sloping edge, (slant height), l, consists of
- A circular base
- A sector with radius, l, and an arc length equal to the circumference of the base

The curved surface area of a cone, A, with radius, r, perpendicular height, h, and sloping edge, l, can be found using the formula
- $A = π r l$
- This formula is given to you in the exam
The total surface area of a cone, A_Total, can be found using the formula
$A_{T o t a l} = π r l + π r^{2}$
This formula is not given to you in the exam

How do I find the surface area of a sphere?

A sphere has a single curved surface

The surface area of a sphere, A, with radius, r, can be found using the formula
- $A = 4 π r^{2}$
- This formula is given to you in the exam

A hemisphere has half the curved surface area of a sphere and the flat circular base

The surface area of a hemisphere, A, with radius, r, can be found using the formula
- $A = 2 π r^{2} + π r^{2}$
- This formula is not given to you in the exam

Examiner Tips and Tricks

The curved surface area for a cylinder, cone and sphere are given to you in the exam
- Read the question carefully, you may need to add additional areas, e.g. a base
- Make you are confident in calculating the areas of rectangles, circles and triangles

Worked Example

A toy consists of a cone of radius 5 cm and slant height 12 cm placed on top of a hemisphere with the same radius. Find the total surface area of the toy. Give your answer to 3 significant figures.

3D toy consisting of a cone on top of a hemisphere

Calculate the curved surface area of the cone using the formula, $A = π r l$

$A_{c o n e} = π \times 5 \times 12 = 60 π$

Calculate the curved surface area of a hemisphere using the formula for the curved surface area of a sphere, $A = 4 π r^{2}$ and dividing it by 2

$A_{h e m i s p h e r e} = \frac{4 π \times 5^{2}}{2} = 50 π$

Add the two areas together to find the total surface area of the toy

$A_{T o t s l} = 60 π + 50 π = 110 π$

Evaluate on your calc and round to 3 significant figures

$A_{T o t a l} = 345.57519 . . .$

346 cm² (3 s.f.)

Last updated: 18 October 2024

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