Unit 9: Areas and volumes of geometrical 3D shapes

Transcription

1 Unit 9: Areas and volumes of geometrical 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.

2 Vocabulary you need in this lesson: You are going to use some vocabulary related to this lesson and the problems you will work with. The same words appear in the crossword, in the word scramble and in the word search.

3 Some theory Pythagoras s theorem In a right angled triangle, the addition of the cathetus squared is equal to the hypotenuse squared. Polyhedra Surface Area: to get the area of a polyhedron, draw its net and add the areas of all the polygons. Volume of prisms and pyramids: the volume of prisms and pyramids can be found using the formulas: V prism base ' s area height V pyramid base ' s area height 3 Solids of revolution Area : r ( g r ).

4 Now it s time to practise Exercises and Problems 1. I have a table that is 2 meters long. There is a lamp hanging above the table. The lamp is hanging exactly 3.5 meters above the center of the table. The light from the lamp illuminates the entire table. How far is it from the lamp to the edge of the table? 2. The building where Mike lives in Chicago is 87m tall. The shadow of the building is 79m long. How far is it from the top of the building to the far end of the shadow? 3. Laura leaves her castle and rides her horse 2 fields east, turns and rides 5 Fields North to go to Mike s Castle. If each field is 1/4 of a mile long, how far is the direct route from Laura 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 a castle. The base of the ladder is 4 feet away from the castle. The wall of Laura s castle is 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:

5 7. Draw the net for a cylinder with a radius of 1.5 cm and a height of 2.5 cm, and mark the measures 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 of solid 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 of 4m. 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, both with 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. Round all answers to hundredths. Use 3.14 for pi. Volume of a cone with height of 9 cm and radius of 7 cm Height of a cone with volume of 132 cubic cm and radius of 3 cm Volume of a cone with diameter 16 cm and height of 4 cm Volume of a cylinder with radius of 5 cm and height of 3 cm Number of vertices on a cone Number of vertices on a cylinder Volume of a sphere with a radius of 3 ft cubic cm cubic ft cubic cm cubic cm cm

6 Some interesting websites! If you want to practice with a test to check what you have learnt, go to: isbn= &chapter=12&headerfile=4&state=na& To pratice with another test about areas and volume click here: isbn= &chapter=12&headerfile=4&state=na To read a bit about different kinds of pyramids, their surfaces and their volumes go to: To read about spheres and their properties, click here: If you want to revise what you have learnt in this lesson, go to: indice2.htm If you want to read more about Pythagoras, the famous Greek mathematician who discovered the theorem you have learnt about go to: