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How to find the volume of a composite figure-cylinder with a hole in the middle
Now lets look at composite figures with a hole in the middle. We have a cylinder in the middle we have is a prism. Instead of adding the two quantities together, we will subtract the two the volume of the cylinder and the volume of the prism. Lets first find the volume of the cylinder. The volume of the cylinder is pi r squared times the height.(πr^2 x height) base area times height. The base area is given so it equals 9π x 5 = 45π. I need to find the volume of the square prism. I'm not given a side of a square, I'm given a measurement that is not the side. Lets investigate to see what this measurement is. This is 3 which means this is 3 and we know a square has right angles, and becomes a 45 45 90 right triangle. So the side of the prism is the hypotenuse of the 45 45 90 square. The side is 3 root 2, That becomes the side. The volume of a square prism will be base area (side^2) times the height. My side is (3√2)^2 x 5 = 18 x 5 = 90. The volume of the square prism equals 90. What do I do next. Instead of adding I subtract because the cylinder is cut out. 45-π -90
How can you subtract these numbers? If you multiply 45 x 3.14 it equals 141.3 - 90 = 51.3 if you are asked for the decimal.
If you are asked for the decimal you stop here and place your units of cm^3. If asked for an estimate round to 51.3 cm^3.
So there is the volume of a composite figure.
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Tagged under: volume,composite figure,geometry,cylinder prism,cylinder,prism
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