Surface Area (Edexcel GCSE Maths: Foundation)

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Naomi C

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Naomi C

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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, pyramids, and prisms?

  • In cubes, cuboids, polygonal-based pyramids, and polygonal-based prisms (ie. pyramids and 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
  • When calculating surface area, it can be helpful to draw a 2D net for the 3D shape in question
    • For example, consider a square-based pyramid where the top of the pyramid is directly above the centre of the base
      • Its net will consist of a square base and four identical isosceles triangular faces
      • Calculate the area of a square and the area of each triangle then add them together

Net of a square-based pyramid

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 rectangleA cylinder and its net
  • The curved surface area (which is a rectangle) 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 is the circumference of the circle, multiplied by the height
    • This formula is not 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 is the area of the curved surface (a rectangle), plus two circles of radius r
    • 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 if it is needed
  • 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
      • It is just the curved surface area formula above, plus the area of a circle

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 if it is needed

Examiner Tip

  • 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

Find the surface area of the cuboid shown below.

q7-1-4-7-medium-edexcel-gcse-maths

Find the area of the face at the front

2 cm × 10 cm = 20 cm2 

Find the area of the face at the side

2 cm × 15 cm = 30 cm2 

Find the area of the face at the top

10 cm × 15 cm = 150 cm2 

There are two of each face
Add together the areas of all 6 faces

20 + 20 + 30 + 30 + 150 + 150 = 400

400 cm2

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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.