Unit 4D:2-3 Dimensional Shapes

Unit 4D:2-3 Dimensional Shapes LT5: I can identify three-dimensional figures. LT6: I can calculate the volume of a cube. LT7: I can calculate the surface area of a cube. LT8: I can calculate the volume of a right prism. LT9: I can identify the two-dimensional shape formed by slicing a three-dimensional figure.

3-Dimensional Shapes

Three-dimensional figures are not flat figures. They have length, width, and height. They are also called solid geometric figures. • The flat surfaces of three-dimensional figures are called faces. • The faces meet at edges. • The edges are line segments. • The edges meet at vertices (plural of vertex).

face cube vertex edge 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 prism face base edge vertex A rectangular prism has 6 faces, 8 vertices, and 12 edges.

Triangular prism base base face face vertex A 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.

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.

vertex Triangular pyramid face base A triangular pyramid has four faces. All faces, including its base, are triangles. It has six edges and four vertices.

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

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

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.

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

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

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

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

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

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

Now it’s your turn to calculate the volume and surface area of a cube. Complete the following worksheet on both sides.

Volume of a Right Prism • A right prism is a prism that has its bases perpendicular to its lateral surfaces. The lateral surfaces (faces that are NOT the bases) must be rectangles to be a right prism. • The formula for finding Volume of a Right Prism is: V = Bh (B is the area of the base) Lateral surface Lateral surface

Introduction • The following video will show you an introduction on how to calculate the volume of a right prism. • Volume of a Right Prism

Practice

Now it’s your turn to calculate the volume of a right prism. Complete the following worksheet stopping when you reach lesson 12-4.

Unit 4D:2-3 Dimensional Shapes