Unit 9:Areas and volumes ofgeometrical 3D shapes

In this lesson you will learn about:

Pythagoras theorem Areas and volumes of prisms, cubes, pyramids,

cylinders, cones ans spheres.

Solving problems related to area and volume.

Vocabulary you need in this lesson:You are going to use some vocabulary related to this lessonand the problems you will work with. The same words appe-ar in the crossword, in the word scramble and in the wordsearch.

Some theoryPythagoras´s theorem

In a right angled triangle, the addition of the cathetus squared is equal tothe hypotenuse squared.

Polyhedra

Surface Area: to get the area of a polyhedron, draw its net and add theareas of all the polygons.

Volume of prisms and pyramids: the volume of prisms and pyramids can befound using the formulas:

.

Solids of revolution3

''

heightareasbaseVheightareasbaseV pyramidprism

)(: rgrArea

Now it´s time to practiseExercises and Problems

1. I have a table that is 2 meters long. There is a lamp hanging above thetable. The lamp is hanging exactly 3.5 meters above the center of the table. Thelight from the lamp illuminates the entire table. How far is it from the lamp to the edge ofthe table?

2. The building where Mike lives in Chicago is 87m tall. The shadow of thebuilding is 79m long. How far is it from the top of the building to the far end ofthe shadow?

3. Laura leaves her castle and rides her horse 2 fields east, turns and rides 5 Fields Northto go to Mike’s Castle. If each field is 1/4 of a mile long, how far is the direct route fromLaura’s castle to Mike’s Castle (in miles)?

4. Mike is attacking Laura’s castle again! A 12-foot ladder is leaning against the side of acastle. The base of the ladder is 4 feet away from the castle. The wall of Laura’s castleis 10 feet high. Does mike’s ladder reach the top in its current position?

5. The edges of a cuboid measure 7m, 4m, and 4m; is it a regular or an irregular prism?What is its surface area? And its volume?

6. Get the surface area and the volume of the shapes below:

7. Draw the net for a cylinder with a radius of 1.5 cm and a height of 2.5 cm, and mark themeasures on it. What is its surface area? And its volume?

8. . Draw the net for a cone with a radius of 2 cm and a slant height (generatriz) of 3.5 cm.What is its surface area? And its volume?

9. . Get the surface area and the volume of the following solids:A cone with a diameter of 6 cm and a height of 4 cm.A cylinder with a height of 4 m and a radius of 50 dm.A sphere with radius of 10 cm.

10. A rectangle with sides of 7 cm and 5 cm rotates around its shortest side. What kind ofsolid do you get? Calculate its surface area and volume.

11. A painter gets £ 1000 to paint a cylindrical tank with a height of 4 m and a diameter of4m. How much will he get to paint a spherical tank with radius of 2 m?

12. . Calculate the volume of the space between two cylinders, one inside the other, bothwith height of 5 m and radii of 4 m and 2 m.

13. Match the descriptions below with an answer given in the list inside the square. Roundall answers to hundredths. Use 3.14 for pi.

Volume of a cone with height of 9 cm and radius of 7 cmHeight of a cone with volume of 132 cubic cm and radius of 3 cmVolume of a cone with diameter 16 cm and height of 4 cmVolume of a cylinder with radius of 5 cm and height of 3 cmNumber of vertices on a coneNumber of vertices on a cylinderVolume of a sphere with a radius of 3 ft

267.95 cubic cm1113.04 cubic ft461.58 cubic cm0235.50 cubic cm14.01 cm

Some interesting websites!

If you want to practice with a test to check what you have learnt, go to:

http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-829637-4&chapter=12&headerFile=4&state=na&

To pratice with another test about areas and volume click here:http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-845773-4&chapter=12&headerFile=4&state=na

To read a bit about different kinds of pyramids, their surfaces andtheir volumes go to:http://www.mathsisfun.com/geometry/pyramids.html

To read about spheres and their properties, click here:

http://www.mathsisfun.com/geometry/sphere.html

If you want to revise what you have learnt in this lesson, go to:

http://thales.cica.es/rd/Recursos/rd99/ed99-0263-02/geometria/indice2.htm

If you want to read more about Pythagoras, the famous Greek mathemati-cian who discovered the theorem you have learnt about go to:http://en.wikipedia.org/wiki/Pythagoras