Unit 4D:2-3 Dimensional Unit 4D:2-3 Dimensional ShapesShapes

LT5: I can identify three-dimensional figures.LT5: I can identify three-dimensional figures.

LT6: I can calculate the volume of a cube.LT6: I can calculate the volume of a cube.

LT7: I can calculate the surface area of a cube.LT7: I can calculate the surface area of a cube.

LT8: I can calculate the volume of a right prism.LT8: I can calculate the volume of a right prism.

LT9: I can identify the two-dimensional shape formed LT9: I can identify the two-dimensional shape formed by slicing a three-dimensional figure.by slicing a three-dimensional figure.

3-Dimensional Shapes3-Dimensional Shapes

Three-dimensional figures are Three-dimensional figures are notnot flat figures. They flat figures. They have length, width, and height. They are also have length, width, and height. They are also

called called solid geometric figures.solid geometric figures.

The flat surfaces of three-The flat surfaces of three-dimensional figures are called faces.dimensional figures are called faces.

The faces meet at edges.The faces meet at edges.The edges are line segments.The edges are line segments.The edges meet at vertices (plural of The edges meet at vertices (plural of

vertex).vertex).

cube

edge

vertex

face

A cube, just like a rectangular prism, has 6 faces (all squares), 8 vertices, and 12 edges.

A prism is named based on what type of base you start with. For example, if you start with a rectangle on the base (bottom) you will have constructed a rectangular prism. If you start with a triangle on the base (bottom) you will have constructed a triangular prism.

Let’s view some examples…

Rectangular prismface

base

vertex

edge

A rectangular prism has 6 faces, 8 vertices, and12 edges.

Triangular prism

face

base

vertexA triangular prism has five faces. Its base is a triangle. (Notice that even when the triangular prism sits on a rectangle, the base is still a triangle.) Two of its faces are triangles; three of its faces are rectangles. It has six vertices and nine edges.

base

face

Just like with prisms, pyramids are also named based on what type of base you start with. For example, if you start with a rectangle on the base (bottom) you will have constructed a rectangular pyramid. If you start with a triangle on the base (bottom) you will have constructed a triangular pyramid.

Let’s view some examples…

Rectangular pyramid

face

vertex

base

A rectangular pyramid has 5 faces. Its base is a rectangle or a square and the other 4 faces are triangles. It has 8 edges and 5 vertices.

Triangular pyramid

face

base

vertex

A triangular pyramid has four faces. All faces, including its base, are triangles. It has six edgesand four vertices.

Cone

A cone is an object that has a circular base and one vertex

height

radiusbase

vertex

Cylinder

A cylinder is a solid object with two identical flat ends that are circular. It also has one curved side.

height

radiusbase

Sphere

A sphere is an object shaped like a ball. Every point on the surface of the sphere is the same distance from the center.

You will now join with a partner to “create” some 3-D shapes. You will be given a table to fill in based on the creation you make. You will be finding the number of faces, edges, and vertices of different pyramids and prisms. Complete the entire table. We will then discuss your findings as a group.

Now it’s your turn to Now it’s your turn to identify the three-identify the three-

dimensional shapes we dimensional shapes we have discussed. have discussed.

Complete the following Complete the following worksheet ONLY worksheet ONLY

identifying what each identifying what each shape is.shape is.

Volume of a CubeVolume of a Cube

The formula for finding Volume of a The formula for finding Volume of a Cube is: V = e³Cube is: V = e³

e

e e

PracticePractice

Find the volume of a cube with sides Find the volume of a cube with sides 12cm.12cm.

PracticePractice

What is the volume of a cube with What is the volume of a cube with sides 4.5in?sides 4.5in?

Surface Area of a CubeSurface Area of a Cube

The formula for finding Surface Area of The formula for finding Surface Area of a Cube is: SA = 6e²a Cube is: SA = 6e²

e

ee

PracticePractice

Find the surface area of a cube with Find the surface area of a cube with sides 6cm.sides 6cm.

PracticePractice

What is the surface area of a cube with What is the surface area of a cube with sides 5.5in?sides 5.5in?

Now it’s your turn to Now it’s your turn to calculate the volume calculate the volume and surface area of a and surface area of a cube. Complete the cube. Complete the

following worksheet on following worksheet on both sides.both sides.

Volume of a Right PrismVolume of a Right Prism

A right prism is a prism that has its bases A right prism is a prism that has its bases perpendicular to its lateral surfaces. The lateral perpendicular to its lateral surfaces. The lateral surfaces (faces that are NOT the bases) must be surfaces (faces that are NOT the bases) must be rectangles to be a right prism. rectangles to be a right prism.

The formula for finding Volume of a Right Prism The formula for finding Volume of a Right Prism is: V = Bh (B is the area of the base)is: V = Bh (B is the area of the base)

LateralsurfaceLatera

lsurface

IntroductionIntroduction

The following video will show you an The following video will show you an introduction on how to calculate the introduction on how to calculate the volume of a right prism.volume of a right prism.

Volume of a Right Prism

PracticePractice

PracticePractice

Now it’s your turn to Now it’s your turn to calculate the volume of calculate the volume of a right prism. Complete a right prism. Complete the following worksheet the following worksheet

stopping when you stopping when you reach lesson 12-4.reach lesson 12-4.