An Introduction to 3-D ShapeSlideshow 16Mathematics, Mr Richard Sasaki, Room 307

Objectives• Recall names of certain elements of

basic shapes• Recall formulae to find attributes to

certain basic shapes• Apply these formulae to finding

missing values for shapes

3D Shapes

CubeCuboid

(Rectangular Prism)

Triangular Prism

Cylinder

Shapes that are flat are called 2D Shapes. We will learn about these in detail in Chapter 5. For now, we will use basic properties.Let’s review some shape names.

The CubeA cube has 6 square faces where 3 meet at each vertex.

𝑙

𝑙

𝑉𝑜𝑙𝑢𝑚𝑒=¿𝑉=¿3

( h𝑙𝑒𝑛𝑔𝑡 )3

𝑙=¿3√𝑉𝑙 Note: means the cube root of the volume.

To find the cube root, we consider what number we cube to make the given number.3√8=¿2 3√1=¿1 3√64=¿4 3√1000=¿10

The CuboidA cuboid has 6 rectangular faces where 3 meet at each vertex.h

𝑙𝑉𝑜𝑙𝑢𝑚𝑒=¿

𝑉=¿𝑙 h𝑤h𝑙𝑒𝑛𝑔𝑡 × h𝑤𝑖𝑑𝑡 ×h h𝑒𝑖𝑔 𝑡

𝑙=¿𝑉h𝑤 𝑤=¿𝑉h𝑙

𝑤

= 𝑉𝑙𝑤

The CuboidExample

A cuboid has width and height 3cm. It’s volume is 63cm3. Calculate its length, .

Let’s label the values given on the cuboid.3𝑐𝑚3𝑐𝑚

=𝑉h𝑤¿633×3¿7𝑐𝑚

𝑙

All calculations are simply substitution!

Answers4𝑐𝑚4𝑐𝑚64 𝑐𝑚3

105𝑐𝑚3

3𝑐𝑚216𝑐𝑚3

1𝑚108𝑐𝑚3

6 4𝑐𝑚3

2𝑚5𝑘𝑚

288𝑐𝑚3

6𝑚𝑚𝑎𝑛𝑑6𝑚𝑚

84 𝑐𝑚3

The CylinderThe cylinder is made up of two parallel circles connected by a curved edge.

h𝑉𝑜𝑙𝑢𝑚𝑒=¿𝑉=¿𝜋𝑟 2h

𝜋× (𝑟𝑎𝑑𝑖𝑢𝑠 )2×h h𝑒𝑖𝑔 𝑡 = √ 𝑉𝜋 h

= 𝑉𝑟 2

𝑟

The Triangular PrismA prism made of two triangles and three rectangles.

𝑉𝑜𝑙𝑢𝑚𝑒=¿𝑉=¿12 h𝑏 𝑙

12×𝑏𝑎𝑠𝑒×h h𝑒𝑖𝑔 𝑡× h𝑙𝑒𝑛𝑔𝑡

𝑏=¿2𝑉h𝑙 h=¿2𝑉𝑏𝑙

𝑏

h

𝑙

𝑙=¿2𝑉h𝑏

The Triangular PrismExample

A triangular prism has base 5cm, height 10cm and length 12cm. Calculate its volume.

Let’s label the values given on the prism.5𝑐𝑚10𝑐𝑚

𝑉=¿12 h𝑏 𝑙¿ 12×5×10×12¿300𝑐𝑚3

12𝑐𝑚

Answers20𝑐𝑚3

240𝑚3

6𝑐𝑚360𝑐𝑚3

60𝑘𝑚3

4 𝑖𝑛

7𝑐𝑚108𝑚𝑚3

1𝑐𝑚

10500𝑐𝑚3