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# Surface Area of Composite Shapes With Holes

Lesson 27 of 37

## Objective: SWBAT find the surface area of composite shapes with holes

*45 minutes*

#### Launch

*10 min*

I'll start the lesson by showing an image of the composite solid block tree. I don't fully understand how this device is used, but I know that it is used for construction. I'll explain that it may be important for the manufacturers to know the exact surface area of each object. Perhaps the tool is coated with a special liquid and the manufacturers need to know how much liquid is used per square unit. I'll then ask students to think about how they could find the surface area of the device. As a prompt, I may ask them to consider the shapes that make up the tool. I'll ask them to discuss these ideas with their partners for about a minute. Students are trying to make sense of the problem to generate generate a way to solve it (**MP1**). I will walk around to listen in to the conversations. I'll try to pick up a few off-based comments and some that are more relevant. I'll want to present both so that students have a chance to critique the reasoning of their classmates (**MP3**). As we discuss answers, I'll try to make sure students bring up the fact that their are 5 large cylindrical holes - we would need to find the lateral surface area of the cylindrical holds. I'll make sure we discuss the rectangular faces as well and discuss in general how to calculate the surface area of the external surfaces. I like this image because it should generate a lot of discussion and help prepare students for the problems to come.

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#### Problem Solving

*15 min*

Now students will find the actual surface area of solids. Note that problem number 3 is meant to be a cylindrical hole. It is kind of difficult to tell based on the drawing. Based on the previous discussion, students should be very well prepared to solve the first 2 problems as they are the same shapes now with dimensions labeled.

The following day is an assessment, so I have included some review problems for students who finish early.

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#### Exit Ticket

*5 min*

I have provided a scaffolded exit ticket to help me assess any breakdowns of understanding. In fact, the first two questions may be the most telling. If a student can't identify the total surfaces, there is probability a visualization issue.

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- LESSON 1: Explore Perimeter and Area of Composite Shapes
- LESSON 2: Perimeter of Irregular Rectilinear Shapes
- LESSON 3: Area of Composite Shapes Using a Grid
- LESSON 4: Area of Composite Shapes
- LESSON 5: Area of Regions Formed by Inscribed Shapes
- LESSON 6: CORNERSTONE:Circle Ratios: Diameter to Radius; Circumference to Diameter
- LESSON 7: CORNERSTONE: Circumference Formula
- LESSON 8: Area of a Circle
- LESSON 9: Circumference & Area Fluency Practice
- LESSON 10: Finding the Radius From a Given Circumference or Area
- LESSON 11: Circumference from Area / Area from Circumference
- LESSON 12: Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments
- LESSON 13: Assessment_Area and Perimeter (Circumference) of Composite Shapes and Circles
- LESSON 14: Drawing Prisms & Pyramids
- LESSON 15: Describe Prisms and Pyramids Using Algebra
- LESSON 16: Using Nets to Find the Surface Area of Prisms
- LESSON 17: Using a Formula to Find the Surface Area of Prisms
- LESSON 18: Finding the surface area of triangular prisms using a net
- LESSON 19: Finding the Surface Area of a Triangular Prism Using A Formula
- LESSON 20: Discovering the Formula for the Surface Area of A Cylinder
- LESSON 21: Finding the Surface Area of Cylinders Using a Formula
- LESSON 22: Practice Day: Surface Area of Prisms & Cylinders
- LESSON 23: Surface Area of Prisms and Cylinders Assessment
- LESSON 24: Finding the Surface Area of Pyramids Using Nets
- LESSON 25: Finding the Surface Area of Pyramids Using a Formula
- LESSON 26: Surface Area of Composite Shapes
- LESSON 27: Surface Area of Composite Shapes With Holes
- LESSON 28: Surface Area Assessment
- LESSON 29: 3-D Models from 2-D Views
- LESSON 30: Exploring Volume and Surface Area with Unifix Cubes
- LESSON 31: Explore Volume of Rectangular Prisms
- LESSON 32: Find the Volume of Prisms Using a Formula
- LESSON 33: Volume Of Cylinders Using a Formula
- LESSON 34: Volume of Composite Shapes
- LESSON 35: Volume and Surface Area - Accelerated Math Fluency Day
- LESSON 36: Volume of Pyramids
- LESSON 37: Surface Area and Volume Final Assessment