solids of revolution - harlem school district 122...geo density and solids of revolution...
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Geo Density and Solids of Revolution ink.notebook
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Solids of Revolution
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Lesson Objectives Standards Lesson Notes
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Solids of Revolution
Geo Density and Solids of Revolution ink.notebook
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May 03, 2018
Lesson Objectives
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Lesson NotesStandards
After this lesson, you should be able to successfully determine the threedimensional figure that is formed by rotating a twodimensional shape around an axis.
Lesson Objectives Standards Lesson Notes
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects.G.GMD.4 Identify the shapes of twodimensional cross sections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.
G.MG.3 Apply geometric methods to solve design problems.
A solid of revolution is a threedimensional figure that is formed by rotating a twodimensional shape around an axis. The line around which the shape is rotated is called the axis of revolution.
For example, if you rotate a triangle about a line that contains one of its sides, the solid of revolution that is produced is a _________.cone
If you rotate a rectangle around a line that contains one of its sides, the solid of revolution that is produced is a ____________.cylinder
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Sketch the solid produced by rotating the figure around the given axis. Then identify and describe the solid.
1.
2.Sketch the solid produced by rotating the figure around the given axis. Then find its volume.
3.
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Because the dimensions of the original figure can be used to describe the solid of revolution, you can use these dimensions to calculate the volume of the solid of revolution.
4.
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Density is the amount of matter that an object has in a given unit of volume. The density of a solid object is a ratio of its mass to its volume.
V = volumem = massD = Density
In science you have seen the density triangle.
DensityDensity Mass
Volume=
DensityMass Volume=
Different materials have different densities, so density can be used to distinguish between materials that look similar. For example, table salt and sugar look alike. However, table salt has a density of 2.16 grams per cubic centimeter, while sugar has a density of 1.58 grams per cubic centimeter.
1. A brick of salt measuring 10.0 cm x 10.0 cm x 2.00 cm has a mass of 433 g. What is its density?
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2. If 500 mL of a liquid has a density of 1.11 g/mL, what is its mass?
3. A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams. A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams. Which metal has the greater density? Round to the nearest hundredth.
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Homework
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2.3.
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4.
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3
7.
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8. 9.Round to the nearest hundredth.
10. 11.
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12.
13. The solid of revolution formed by rotating this pentagon 360°about the given axis is a composition (combination) of what two common solids?
a) two cones b) a sphere and a cylinder
c) a cone and a sphere
d) a cone and a cylinder
14.
a) Find dimensions and volume if rotated around the xaxis.
b) Find dimensions and volume if rotated around the yaxis.
15.
a) Find dimensions and volume if rotated around the xaxis.
b) Find dimensions and volume if rotated around the yaxis.
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16.
a) Find dimensions and volume if rotated around the xaxis.
b) Find dimensions and volume if rotated around the yaxis.
17.
a) Find dimensions and volume if rotated around the xaxis.
b) Find dimensions and volume if rotated around the yaxis.
18. Complete the statement with the word always, sometimes, or never.
The intersection of a plane and a cylinder is
__________________ a rectangle.
19. A block of gold with a mass of 9,660 kilograms has a volume of 0.5 cubic meters. What is the density of gold?
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20. The density of seawater is about 0.001027 kg/cm3. A tropical fish tank measures 50.8 centimeters by 30.5 centimeters by 30.5 centimeters. What is the mass of the seawater in the tank? Round to the nearest hundredth if necessary.
21. Each side of a cube measures 3.9 centimeters. Its mass is 95.8 grams. Find the density of the cube. Round to the nearest hundredth if necessary.
22. The volume of a ball is 768 cm3 and its density is 3.2 g/cm3. What is the mass of the ball? Round to the nearest tenth if necessary.
23. A solid rectangular box has a length of 6 cm, a width of 4 cm and a height of 5cm. Work out the density of the box if the mass of the box is 200g. Round to the nearest hundredth.
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24. Work out the mass of this triangular prism if the density is 3 g/cm³.
Answers:
3
7
7. 9. 8
8
1607.68cylinder
1.6
8
cylinder
3.
7
sphere
5.
cone with a conecut out of thebase
11.2
2
2
16.7513. D 15a)
5
3
235.5
15b) 3
5
141.3
17a) 17b)
53
47.1
35
78.5
19. 19320 kg per m3
21. 1.61 g per cm3
23. 1.67 g per cm3