1 Measurement - Nets, Surface Area and Volume. Terms

Transcription

1 1 Measurement - Nets, Surface Area and Volume Terms

2 2 Measurement - Nets, Surface Area and Volume Nets 1. Draw a net for the following shape. Include all measurements and symbols

3 3 Measurement - Nets, Surface Area and Volume One diagram below is the net of a right cylinder. Predict which diagram is a net. Using the pre-cut net at the station, see if you were correct. Circle the correct net below. 7. Match the net in Set A to the object in Set B. Cross out the two objects that have no available net. Fold Samples if Necessary.

4 4 Measurement - Nets, Surface Area and Volume 8. Draw a net for each of the following containers. Include all measurements. d)

5 5 Measurement - Nets, Surface Area and Volume Surface Area 1. Here is the net of a right rectangular prism. The area of each face is given. What is the surface area of the prism? How did you find this out? 2. Sketch a net of this right rectangular prism. What is its surface area? 3. Find the surface area for each right rectangular prism. Area of Top = X 2 = Area of Sides = X 4 = Area of Top/ Bottom + Area of All Sides = Surface Area + = b) Area of Top = X 2 = Area of Front = X 2 = Area of Sides = X 2 = Area of Top/ Bottom + Area of Front/Back + Area of Sides = Surface Area + + =

6 6 Measurement - Nets, Surface Area and Volume 4. Alan is painting the walls and ceiling of his room, which is 4.2 m long, 3.7 m wide, and 2.6 m high. The window is 60 cm on long by 40 cm high. The door is 2 m high by 85 cm wide. a. Determine the surface area of the walls in the room. (Hint: area of door and window aren t included) b. He will use two coats of paint. A 4-L can of paint covers 36 m 2. How many cans of paint does he need to buy? 5. Here is the net of a right triangular prism. The area of each face is given. What is the surface area of the prism? How did you find this out? 6. Here is a right isosceles triangular prism. Which faces are congruent and share the same area? How do you know?

7 7 Measurement - Nets, Surface Area and Volume 7. Sketch a net of this triangular prism. What is its surface area? Area of Triangle = X 2 = Area of Rectangle 1 = X 1 = Area of Rectangle 2= X 1 = Area of Rectangle 3 = X 1 = Area of Triangles + Area of Rec 1 + Area of Rec 2 + Area of Rec 3 = Surface Area = 8. Calculate the area of the net. How does the area of the net compare to the surface area of the prism formed by the net in questions 5, 7, & 8? 9. Calculate the surface area for each triangular prism. a. b.

8 8 Measurement - Nets, Surface Area and Volume 10. Daniel wants to cover the outside of an empty 3-ring binder with plastic. Each dimension of the binder has been written to one decimal place. How much plastic is needed to cover the outside of the binder? What assumptions do you make? 11. Here is the net of a right cylinder. Find the length of the missing side on the rectangle. a. b. 12. Calculate the surface for each of the right cylinders in question 11. a. Area of Circle = X 2 = Area of Rectangle = X 1 = Area of Circles + Area of Rectangle = Surface Area + = b. Area of Circle = X 2 = Area of Rectangle = X 1 = Area of Circles + Area of Rectangle = Surface Area + =

9 9 Measurement - Nets, Surface Area and Volume 13. Calculate the area of the curved surface of the cylinder. a. b. 14. a) Draw a net for one of the cylinders in question 13. b) Calculate the surface are for this cylinder. 15. A can of frozen juice that is 6.7 cm in diameter and 11.8 cm high is made of a cardboard tube, and a metal top and metal bottom. Suppose 24 cans are recycled. a. Determine how much cardboard is recycled. b. Determine how much metal is recycled.

10 10 Measurement - Nets, Surface Area and Volume 1. The base area and height of each prism is given. Find the volume of each prism. Volume 2. A box of laundry detergent has dimensions of 28 cm by 16 cm by 25 cm. a. Sketch the box. b. What volume of detergent will fill the box? Label with dimensions. 2. a) Determine the volume of prism A. b) Do you need to calculate to determine the volume of prism B? Explain. 3. Find the volume of each rectangular prism. a) Area of Base X Height of Object = Volume Area of Base X Height of Object = Volume c) Area of Base X Height of Object = Volume

11 11 Measurement - Nets, Surface Area and Volume 4. What is the volume of a rectangular prism that has a length of 1.2 meters, a width of 1.2 meters, and a height of 0.5 meters? 5. Sam has a small container of ice cream which is full. How much ice cream is left in the container? 6. In order to build a strong brick fence, Will designed his solid cement bricks to interlock with one another. What is the amount of cement needed for each brick? 7. The amount of water in a rectangular pool is 2000 m 3. The size of the pool is 1000 m 2. What is the depth of the pool? 8. Suppose a milk carton is 10 cm wide and 10 cm long. How tall must the carton be to hold 1 L of milk? (1 cm 3 = 1 ml) 9. Each rectangular prism is divided into 2 congruent triangular prisms along the diagonal shown. The volume of each rectangular prism is given. Find the volume of each triangular prism.

12 12 Measurement - Nets, Surface Area and Volume 10. The base area and length of each triangular prism are given. Find the volume of each prism. Area of Base (triangle) X Height of Object = Volume Area of Base triangle X Height of Object = Volume 11. How do you know which lengths on a triangle are the ones used to calculate the area for that triangle? 12. Find the volume of each triangular prism. Area of Base triangle X Height of Object = Volume Area of Base triangle X Height of Object = Volume c) cm 3 _

13 13 Measurement - Nets, Surface Area and Volume 13. Mr. Munro has a wedge of cheddar cheese. He plans to serve the cheese as an appetizer before dinner. a. What volume of cheese does Mr. Munro have? b. Suppose each person eats 20 cm 3 of cheese. How many people will the cheese serve? 14. The volume of a triangular prism is 50 m 3. The length of the prism is 5 m. What is the area of each triangular face? 15. The base area and height of each cylinder are given to one decimal place. Calculate the volume of each cylinder. Area of Base(circle) X Height of Object = Volume Area of Base circle X Height of Object = Volume Area of Base circle X Height of Object = Volume 16. Calculate the volume of each cylinder. c)

14 14 Measurement - Nets, Surface Area and Volume 17. A hockey puck is a solid piece of rubber with dimensions shown. How much rubber is used to make a hockey puck? 18. There are 12 people in Mandy s exercise class. Each one has a water bottle like this. They will their bottles from a water cooler that is 20 cm in radius and 90 cm in height. Estimate how many times they can fill up their water bottles before the cooler needs to be refilled. 19. A cylindrical candle mold is 5 cm in diameter and 7 cm tall. How much wax would be needed to make 25 candles? 20. The curved surface area of a solid cylinder is 660 cm 2. The cylinder height is 10 cm. a. What is the circumference of the cylinder? b. What is the radius of the cylinder? c. What is the area of one circular base? d. What is the surface area of the cylinder? 21. a) What is the formula for the volume of right prisms and right cylinders? b) How do you know what face is the base of each of these shapes?