Surface Area

Surface Areavideo

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

• You should remember the formula for the area of a rectangle, but you are given the area of a triangle in your exam

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

  • $A=2\pi \mathit{ }r h$

  • This formula is given to you in the exam

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

  • $A_{Total}=2\pi \mathit{ }r\mathit{ }h+2\pi \mathit{ }{r}^2$

  • 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

  • $A=\pi \mathit{ }r l$

  • This formula is given to you in the exam

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

• $A_{Total}=\pi \mathit{ }r l\mathit{+}\pi \mathit{ }{r}^2$

• 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

  • $A=4\pi \mathit{ }{r}^2$

  • 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

  • $A=2\pi \mathit{ }{r}^2+\pi \mathit{ }{r}^2$

  • This formula is not given to you in the exam