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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.
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