Welcome to Clip from Spiral logo

Interactive video lesson plan for: Finding the volume of a composite figure

Activity overview:

Geometry Teachers Never Spend Time Trying to Find Materials for Your Lessons Again!

Join Our Geometry Teacher Community Today!
How to find the volume of composite shapes. Think of composite figures as two or more shapes combined.

A composite figure is a geometric figure composed of two or more geometric figures. Think of a house from the Monopoly game. The house is composed of a prism and a triangular prism. The key to finding the volume of these composite figures is to identify the different shapes involved, calculate their volume and then add these separate volumes together.

The first example involves a composite figure with a triangular prism placed above a rectangular prism.

The second example involves finding the volume of a composite figure that is a combination of rectangular prism topped of with half a cylinder.

Today we are going to find the volume of composite figures. Find the volume of a rectangular prism. What kind of figures do we have? Well at first we have that is a pyramid and a prism on the bottom, but be careful. The top is also a prism because because it has parallel bases , but the bases happen to be triangles. What you need to do is find the area of the rectangular prism on the bottom. We know that is easy,it is length times width times height. Let's do that.That will be 8x4x5 which equals 160 cubic centimeters. So 160 cubic centimeters. Now let's find the volume of the regular triangular prism. This triangle here,notice how they are parallel to each other. We need to find the area of an equilateral triangle. Draw our altitude which cuts the triangle into 4 and 4. This is the short leg,this is the long leg,so that is 4√3 So to find the area take 1/2(8)(4√3) = 16√3 and that becomes my base area. Base area times the height because here is my parallel side so times 5 and 16 x 5 = 80 so 80√3 cm^3 Here are my two volumes, and I will add them. Can I add them together, no because of the form they are in. So this will be your answer in exact form. If you have a decimal form you can go ahead and type it out as 160 +80 and put in √3 and it should give you the decimal answer which is 298.6 cubic centimeters. Here is the exact. If you want an exact answer we would have to round it off then here is the exact answer. If you are asked for exact answers leave them as radicals,if you are asked for estimated answers you can use decimals. Let's look at another composite figure. This next composite figure is a rectangle prism topped off with a cylinder. What do you notice about the cylinder? It is only half a cylinder. Let's look at the rectangular prism, and then we will figure out the rectangle part. The rectangular prism is length x width x height or 9 x 11 x 6 = 99 x 6 = 594 cubic millimeters. That part is easy,the rectangular prism,now let's look at the cylinder. The cylinders volume is Πr^2 x height. Because we only have half of it we will divide it by 2. Let's go back and figure our radius and our height. What is the radius of this cylinder? It is half this side. So this side 9 and this is 9, so it will be 41/2. 4.5^2 is the radius and 11 will be our height which equals ( Π4x5 x 11)/2 and this equals 222.75 Π/2 which equals 111.375 pi is the volume of the cylinder part. Now we have to add these two together which becomes 594 + 111.375Π , (we usually add to tenths)and because this has a pi I can't add these together, and I will stick my units with it, and it will be in millimeters cubed.

At MooMooMath we provide helpful Math and Geometry videos to help you figure out how to solve Math problems or review old Math concepts you may need to refresh. If you’re a Math student or teacher, we'd love to have you subscribe and join us! We upload a new video every day
* Subscribe

Let’s connect
* Google+
* Pinterest

Please watch: "Study Skills Teacher's Secret Guide to your Best Grades"

Tagged under: Volume (Dimension),composite figure,geometry,volume composite figure,moomoomath,compound shapes.,shapes,geometric shapes,volome geometric shapes

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share Finding the volume of a composite figure on Google+ Share Finding the volume of a composite figure on Twitter Share Finding the volume of a composite figure on Facebook Pin Finding the volume of a composite figure Email Finding the volume of a composite figure

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.


Carry out a quickfire formative assessment to see what the whole class is thinking


Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices


Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome