Surface Area

Slideshow 49, MathematicsMr Richard Sasaki

Room 307

Objectives• Review how to find the area of

various polygons• Learn how to calculate the

surface area of cuboids, triangular prisms and square-based pyramids

• Learn how to calculate the surface area of a cylinder

Answers15𝑐𝑚2 49𝑐𝑚2 8𝑐𝑚2

108𝑐𝑚2 91𝑐𝑚2 70𝑐𝑚2

26𝑐𝑚2 135𝑐𝑚2 204 𝑐𝑚2

Surface AreaWhat is surface area?The total area of faces & surfaces on a 3D shape.Calculating surface area for cuboids and triangular prisms is easy as long as we know the dimensions of each face.

5𝑐𝑚 2𝑐𝑚3𝑐𝑚

5𝑐𝑚 2𝑐𝑚3𝑐𝑚2𝑐𝑚3𝑐𝑚

Surface Area - Cuboid

5𝑐𝑚 2𝑐𝑚3𝑐𝑚

5𝑐𝑚 2𝑐𝑚3𝑐𝑚2𝑐𝑚

3𝑐𝑚

All we do is add the total area of each face.

10𝑐𝑚215𝑐𝑚210𝑐𝑚26𝑐𝑚2 6𝑐𝑚215𝑐𝑚2

We just simply add the numbers together.10+15+10+15+6+6¿20+30+12

¿62𝑐𝑚2

Triangular PrismVisualising a net is always good!

4𝑐𝑚10𝑐𝑚

5𝑐𝑚

3𝑐𝑚

10𝑐𝑚4𝑐𝑚3𝑐𝑚5𝑐𝑚3𝑐𝑚

4𝑐𝑚

Surface Area: (10 ∙4 )+¿(10 ∙3 )+¿(10 ∙5 )+¿(0.5 ∙ 4 ∙3 ) ∙2¿ 40+¿30+¿50+¿12¿132𝑐𝑚2

2 (1∙1 )+4 (3 ∙1 )=14 𝑐𝑚2

(5 ∙10 )+(5 ∙8 )+ (5 ∙6 )+2 (0.5 ∙6×8 )¿168𝑐𝑚2

6 (6 ∙6)=216𝑐𝑚2

(12 ∙5 )+(12∙ 4 )+ (12 ∙3 )+2 (0.5 ∙3×4 )¿156𝑐𝑚2

2 (2 ∙8 )+2 (11 ∙8 )+2 (2 ∙11 )=252𝑐𝑚2

(7 ∙13 )+(7 ∙12 )+(7 ∙5 )+2 (0.5 ∙5×12 )¿270𝑐𝑚2

Square-Based PyramidsLet’s have a look at the square based pyramid.

𝑎𝑎𝑙

𝑎𝑎𝑙

This should be easy to calculate the surface area with too!

Example

4𝑐𝑚7𝑐𝑚

4𝑐𝑚7𝑐𝑚

Surface Area:

42+¿(4 ∙7 ∙ 12 )∙ 4¿16+56¿72𝑐𝑚2

Square-Based Pyramids

40𝑐𝑚2 45𝑚2 161𝑚𝑚2

56𝑐𝑚2 105𝑘𝑚2 1035𝑘𝑚2

Let’s calculate the surface area of a cylinder with its radius and length.Example

𝑟𝑙

¿2𝑚¿10𝑚

We know the cylinder is made of two and, if flattened a

.

circlesrectangl

e

2𝑚10𝑚

𝐶=2𝜋 𝑟4𝜋𝑚

Cylinders

2𝑚10𝑚

𝐶=2𝜋 𝑟4𝜋𝑚

S.A =

¿8𝜋+40𝜋¿ 48𝜋𝑚2

Note: Formulae for surface area will not be provided on the test as calculations are simply sums of areas of polygons and circles. Some formulae for polygons and circles will be provided.

Cylinders

48𝜋𝑐𝑚2 152𝜋𝑐𝑚2 84 𝜋𝑚2

3.5𝜋𝑚2 480𝜋𝑚𝑚2 16𝜋 𝑘𝑚2

Answers