Demystifying Surface Area and Volume

Transcription

1 Demystifying Surface and Volume CYLINDER 1. Use the net of the cylinder provided. Measure in centimeters and record the radius of the circle, and the length and width of the rectangle. radius = length = width = 2. Cut out the circles and rectangle. Use tape and construct the cylinder. Sketch a picture of your cylinder in the space below: 3. The rolled up rectangle is called the lateral face of the cylinder. What shape is the base of the cylinder? How do you know what is the base? Can you have more than one shape as a base? Explain. 4. Calculate the circumference of the cylinder. How does this value compare to the dimensions of the rectangle? Explain. 5. The amount of paper used to make a cylinder is the surface area. How can you calculate the surface area of your cylinder? Explain. 6. What is the area of each region and total surface area? Include the units of measurement. Circles Rectangle Total Surface Demystifying Surface and Volume Student Materials Page 1 of 9

2 7. When you fill a cylinder with something, such as plain M & M s, you are finding volume. Remember, to calculate volume, multiply the area of the base times the height of the cylinder. What measurement from part 1 above corresponds to the cylinder s height? 8. What is the volume of your cylinder? (Remember to include the appropriate units) Volume = 3 9. If 60 plain M & M s take up 12 cm of space, approximately how many M & M s would fill your cylinder? Explain and show your work. Demystifying Surface and Volume Student Materials Page 2 of 9

3 RIGHT TRIANGLE PRISM 1. Use the net provided for a right triangle prism. Measure in centimeters the dimensions of the right triangles and rectangles. Triangles Length Width Rectangle A Rectangle B Rectangle C 2. Cut out the net of triangles and rectangles. Use tape and fit together the net to make a triangular prism. Sketch below 2 different orientations of the prism: 3. What shape is considered the base of this prism, regardless of its orientation? Explain how and why this shape makes sense. 4. The shapes that connect the bases are called lateral faces. What shapes are the lateral faces, and are they all the same size? 5. What measurement do all of the lateral faces have in common? What does this measurement mean with respect to the prism? Demystifying Surface and Volume Student Materials Page 3 of 9

4 6. Measure in centimeters, the hypotenuse of the right triangle with a ruler. What measurement does this correspond to from question number 1? 7. The amount of paper used to make a triangular prism is the surface area. How can you calculate the surface area of your triangular prism? Explain. 8. What is the area of each piece and total surface area? What are the units of measurement? Triangles Rectangle A Rectangle B Rectangle C Total Surface 9. When you fill a prism with something, such as plain M & M s, you are finding volume. To calculate volume, multiply the area of the base times the height of the prism. Calculate the volume of your triangular prism, show work. Volume = Tom, a friend in your class, is confused. He knows that the area of a triangle is bh, 2 and that volume involves height. He does not know which one to use when. Help him out and explain the difference between them. Demystifying Surface and Volume Student Materials Page 4 of 9

5 3 11. If 60 M & M s take up 12 cm of space, approximately how many M & M s would fill your triangular prism? Explain and show your work 12. Earlier in this lesson, you found the three sides of a triangle by measuring with a ruler. Jane says that if you know the two legs of the right triangle base, you can easily find the third side without measuring with a ruler. Why does she think this? Do you agree with Jane? Demystifying Surface and Volume Student Materials Page 5 of 9

6 RECTANGULAR PRISM 1. Use the net provided of the rectangular prism. Measure in centimeters the dimensions of all the rectangles. Rectangles A Length Width Rectangles B 2. Susan wants to use base and height instead of length and width when she measures the dimensions of the rectangles. Is this okay? Explain 3. Cut out the net of the rectangular prism. Use tape and fit together to make the prism. Sketch below 2 different orientations of the prism: 4. What shape will all the bases and lateral faces be? Does it matter which orientation you use to determine surface area or volume? Explain why or why not. 5. How can you determine the surface area of your rectangular prism? Demystifying Surface and Volume Student Materials Page 6 of 9

7 6. Calculate the area of each face of your prism; be sure to include your units. How many of each rectangle do you need? Rectangles A Rectangles B Total Surface 7. Meagan remembers from middle school that you can determine volume of a rectangular prism by calculating length times width times height. She is having trouble figuring out how to look at her prism and determine which side is which. How would you help her? Explain. 8. If you calculated volume by multiplying the area of the base times the height, would you get the same answer as Meagan? Which dimension would you use as the height? Explain If 60 M & M s take up 12 cm of space, approximately how many M & M s would fill your rectangular prism? Show your work. 10. Look around the classroom, around your school, or outside. Are there any examples of cylinders or triangular prisms you can see? List them below: Demystifying Surface and Volume Student Materials Page 7 of 9

8 Skateboard Parks and Camping: Surface and Volume in the real world One of the more popular locations for prisms is a skateboard park. A ramp is drawn in the space below. The height of the ramp is 6 feet, the skating width is 5 feet, and the entire length of the ramp along the ground is 20 feet. Mark the picture below with these dimensions. 1. The ramp is a combination of a rectangular prism and right triangle prism. Do you have enough information to determine the surface area of the entire ramp structure? Explain. 2. If the top of the ramp is a rectangle with dimensions of 5 feet by 7 feet, calculate the surface area of the ramp structure. Is there a hidden side of the rectangular prism that is not going to be used in this calculation? What about in the triangular prism? Explain. 3. Calculate the volume of the skateboard ramp. Do you need to worry about the hidden faces when you calculate volume? Explain. 4. Your friend Brian thought this ramp was pretty cool and decided that he wanted to make one at home out of plywood. He already has the framework made and has to add sheets of plywood to finish it. Which calculation would he want to use, the surface area or volume? Would the hidden side(s) be necessary for construction? Explain. 5. If plywood is sold in sheets that are 8 feet by 4 feet, and they cost $ a sheet, how much would Brian have to pay in order to make the ramp? 6. Most ramps at skateboard parks are poured concrete. Concrete is sold in cubic yards, so how much concrete would be needed to make this ramp? If the cost of concrete is $12.75 a cubic yard, what would be the total cost? Demystifying Surface and Volume Student Materials Page 8 of 9

9 Betty loves to go camping. Her family has a tent that used to be her grandfathers. It is made of olive green canvas material, and looks like an isosceles triangular prism when it is set up. Betty drew a picture of it below: 7. What shape is the floor of the tent? Is this the base or the height of the prism? Explain. 8. Betty knows that the floor of the tent is 12 feet by 8 feet, with the front being the longest. She also knows that she cannot stand up inside the tent without hitting her head. She estimates that the peak of the tent is 5 feet. Calculate the length of the legs of the isosceles triangle in feet, show work. 9. How much olive green canvas material does it take to make Betty s tent, including the floor? 10. Betty hates mosquitoes. She has a bug spray that claims to kill mosquitoes in the 3 immediate area, 10 in per pump of spray. Ignoring the volume of Betty, how many pumps of spray should she use inside the tent to ward off the mosquitoes? Demystifying Surface and Volume Student Materials Page 9 of 9