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Surface Area (Edexcel IGCSE Maths A (Modular))

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Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Edexcel Maths A (Modular): Higher Unit 2Edexcel Maths A: HigherCambridge (CIE) International Maths: ExtendedCambridge (CIE) International Maths: CoreCambridge (CIE) Maths: CoreCambridge (CIE) Maths: Extended

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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

    A cylinder and its net

  • The curved surface area of a cylinder, A, with base radius, r, and height, h, is therefore given by

    • A equals 2 pi italic space r space h

    • This formula is given to you in the exam

  • The total surface area of a cylinder, ATotal, can be found using the formula

    • A subscript T o t a l end subscript equals 2 pi italic space r italic space h plus 2 pi italic space r squared

    • 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

A cone and its net

  • 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 equals pi italic space r space l

    • This formula is given to you in the exam

  • The total surface area of a cone, ATotal, can be found using the formula

  • A subscript T o t a l end subscript equals pi italic space r space l italic plus pi italic space r squared

  • 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

A sphere

  • The surface area of a sphere, A, with radius, r, can be found using the formula

    • A equals 4 pi italic space r squared

    • 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

Surface area of a hemisphere

  • The surface area of a hemisphere, A, with radius, r, can be found using the formula

    • A equals 2 pi italic space r squared plus pi italic space r squared

    • 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 equals pi italic space r italic space l

A subscript c o n e end subscript equals pi cross times 5 cross times 12 equals 60 pi

Calculate the curved surface area of a hemisphere using the formula for the curved surface area of a sphere, A equals 4 pi italic space r squared and dividing it by 2

A subscript h e m i s p h e r e end subscript equals fraction numerator 4 pi cross times 5 squared over denominator 2 end fraction equals 50 pi

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

A subscript T o t s l end subscript equals 60 pi plus 50 pi equals 110 pi

Evaluate on your calc and round to 3 significant figures

A subscript T o t a l end subscript equals 345.57519...

346 cm2 (3 s.f.)

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.