Surface Area

Slideshow 49, Mathematics

Mr 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

Answers

15𝑐𝑚249𝑐𝑚28𝑐𝑚2

108𝑐𝑚291𝑐𝑚2

70𝑐𝑚2

26𝑐𝑚2

135𝑐𝑚2204 𝑐𝑚2

Surface Area

What 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.

5 cm

2 cm

3 cm 5

cm

2 cm

3 cm

2 cm

3 cm

Surface Area - Cuboid

5 cm

2 cm

3 cm 5

cm

2 cm

3 cm

2 cm

3 cm

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

10 cm2

15 cm2

10 cm2

6 cm2 6 cm215 cm2

We just simply add the numbers together.10 + 15 + 10 + 15 + 6 + 6

= = =

Surface Area – Triangular Prism

Visualising a net is always good!

4 cm

10 cm

5 cm

3 cm

10 cm

4 cm3 cm5 cm3 cm

4 cm

Surface Area: (10 ∙4 )+¿(10 ∙3 )+¿(10 ∙5 )+¿(0.5 ∙ 4 ∙3 ) ∙2

= 30+¿50+¿12=

Answers

14𝑐𝑚2

168𝑐𝑚2 216𝑐𝑚2

156𝑐𝑚2252𝑐𝑚2 270𝑐𝑚2

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

𝑎𝑎𝑠

𝑎𝑎𝑠

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

Square-Based PyramidsExample

4𝑐𝑚

7𝑐𝑚4𝑐𝑚

7𝑐𝑚

Surface area =

42+¿(4 ∙7 ∙ 12 )∙ 4¿16+56¿72𝑐𝑚2

CylindersLet’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

On your test you won’t receive any formulae for surface area as the calculations are somewhat obvious but you are welcome to remember some if you need to!

Answers

40𝑐𝑚2 45𝑚2 161𝑚𝑚2

56𝑐𝑚2 105𝑘𝑚2 1035𝑘𝑚2

Answers

48𝜋𝑐𝑚2 152𝜋𝑐𝑚2 84 𝜋𝑚2

3.5𝜋𝑚2 480𝜋𝑚𝑚2 16𝜋𝑘𝑚2