Surface Area (Edexcel IGCSE Maths)

Spec point — 4.10D

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

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(which is a rectangle) of a cylinder, A, with base radius, r, and height, h, is therefore given by

  • $A=2πrh$
  • 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, A_Total, can be found using the formula

  • $A_{Total}=2πrh+2πr^{2}$
  • 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

• The curved surface area of a cone, A, with radius, r, perpendicular height, h, and sloping edge, l, can be found using the formula

  • $A=πrl$
  • This formula is given to you in the exam if it is needed

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

  • $A_{Total}=πrl+πr^{2}$

  • 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

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

  • $A=4πr^{2}$
  • This formula is given to you in the exam if it is needed

Exam Hint

• 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.

Answer:

Find the area of the face at the front

*2 cm × 10 cm = 20 cm ² *

Find the area of the face at the side

*2 cm × 15 cm = 30 cm ² *

Find the area of the face at the top

*10 cm × 15 cm = 150 cm ² *

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

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

Final answer: 400 cm²