Area of Circles. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and record in the blanks above.

Transcription

1 Name: Area of Circles Label: Length: Label: Length: A Part 1 1. Label the diameter and radius of Circle A. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and recd in the blanks above. 3. What do you notice about the relationship between the diameter and the radius? Part 2 1. Use a yellow highlighter to shade the area of Circle A. 2. Locate and recd the fmula f the area of a circle. 3. How could you write the fmula f the area of a circle without using exponents? 4. Fill in the blanks with the appropriate wds to determine the area of a circle. Area = 5. Fill in the blanks with the appropriate numbers to determine the area Circle A. Area = 6. Find the area of Circle A.

2 Name: Layers upon Layers = 1 square centimeter 1. What is the area of the shaded polygon? 2. Use centimeter cubes to cover the shaded region. How many centimeter cubes are needed to cover the shaded region? What is the height of the three-dimensional figure created by the cubes? 3. Continue to stack layers of cubes onto the first layer and recd the infmation in the table below. Area of the Base Number of Layers Height Process Total Number of Cubes How many cubes would you need if there were eight layers? Twenty-two layers? 5. How did you determine the total number of cubes that were needed in Question 4? 6. What mathematical term could be used to describe the total number of cubes in the three-dimensional figure?

3 Name: Layers upon Layers* = 1 square centimeter 1. What is the area of the shaded polygon? 2. Use centimeter cubes to cover the shaded region. How many centimeter cubes are needed to cover the shaded region? What is the height of the three-dimensional figure created by the cubes? 3. Continue to stack layers of cubes onto the first layer and recd the infmation in the table below. Area of the Base Number of Layers Height Process Total Number of Cubes How many cubes would you need if there were eight layers? Twenty-two layers? 5. How did you determine the total number of cubes that were needed in Question 4? 6. What mathematical term could be used to describe the total number of cubes in the three-dimensional figure?

4 Name: Building on Bases F each figure below, find the area of the shaded region and recd your answer in the blank. Use the areas to answer the questions below. (Note: Each represents one square centimeter.) Base A Base C Area of Base Area of Base Base B Base D Area of Base Area of Base 1. If it were possible to cut a centimeter cube in parts, what would be the volume (total number of cubes) if there were 3 layers stacked on the shaded region of Base A: Base B: Base C: Base D: 3-Dimensional Figure: 3-Dimensional Figure: 3-Dimensional Figure: 3-Dimensional Figure:

5 2. Describe the process used to determine the total number of cubes when the area of Base A, B, C, and D were stacked 3 layers high. 3. Lisa has a container in the shape of a triangular prism, as shown below. Highlight the base area in yellow and highlight the height of the prism in blue. 3 cm 10.2 cm 3 cm What is the volume of the container? 4. Mrs. Epstein used a container in the shape of a cylinder to hang on the wall and fill with flowers. The diagram below shows the dimensions of the container. Highlight the base area in yellow and highlight the height of the cylinder in blue. What is the approximate volume of the container? Use ft 3 ft 5. If Base B represents the base of a triangular prism that has a volume of 40 cubic units, what is the height of the prism? How do you know? 6. If Base A represents the base of a triangular prism with a volume of 45 cubic units, what is the height of the triangular prism? How do you know? 7. Using the measurements given in the table below, complete the missing infmation. Label with the crect units. Three- Dimensional Figure Rectangular Prism Area of the Base (B) Height (h) 2.5 cm 9.6 cm³ Cylinder 9 cm² 3 cm Triangular Prism 10 cm² 21 cm³

6 Name: Notes Page Three-Dimensional Figure Name of Three- Dimensional Figure Fmula f the Area of the Base (B) Fmula 10 cm 3 cm 3 cm 3 cm 10 cm 10 cm 3 cm 2.5 cm Region 4 Education Service Center Suppting STAAR Achievement: Grade 7

7 Notes Page Cards Cut along the bold dotted lines. Four sets of cards are provided. V Bh 2 V r h V V Bh bh 2 triangle h prism V Bh V lw h V Bh 2 V r h V V Bh bh 2 triangle h prism V Bh V lw h V Bh 2 V r h V V Bh bh 2 triangle h prism V Bh V lw h V Bh 2 V r h V V Bh bh 2 triangle h prism V Bh V lw h

8 Name: Circuit Recding Sheet 1. Cut out Circuit Cards and glue one card into the first box. 2. Solve the bottom half of the card. Show all wk and recd your answer. 3. The answer to the problem on the first card will be found on the top half of another card. The answer to your first card will be your second card. 4. Glue the second card in the box labeled second card. 5. Continue until all cards have been wked in der. Card Wk Solution

9 Card Wk Solution

10 Cut along the dotted lines. Circuit Cards A cylindrical bird food container is half full of bird food, as shown below. What is the approximate volume in cubic inches of the bird food in the 10 in. container? 10 in. Gustavo made a ceramic container in the shape of a cylinder. The diagram below shows the dimensions of the container. 4 in. 12 in. What is the approximate volume in cubic inches of the container? A company delivers espresso in boxes shaped like rectangular prisms that are 12.5 inches long, 8.3 inches wide, and 2 inches high. What is the volume in cubic inches of 2 boxes? The base of a triangular prism is shown below. Use your ruler to measure the base and height of the triangle to the nearest half centimeter. If the height of the triangular prism is 3.75 cm, determine the volume in cubic centimeters of the triangular prism Grace has a container in the shape of a cylinder to ste her candy. The height of the candy dish is 6 centimeters. If the volume of the container is cubic centimeters, what is the area in square inches of the base? A company developed a box in the shape of a triangular prism, as shown below. What is the volume of the box? 9 ft 2 ft 2 ft The volume of the triangular prism below is 30 cubic units. 4 units What is the area of the base in square units?

11 Cut along the dotted lines A cylindrical bird food container is half full of bird food, as shown below. 10 in. What is the approximate volume in cubic inches of the bird food in the 10 in. container? Circuit Cards With Hints* Hint Are you trying to find the volume of the entire container the volume of the bird seed contained in the food container? Is there any extra infmation? What shape is the base? What is the fmula f the area of the base? A company delivers espresso in boxes shaped like rectangular prisms that are 12.5 inches long, 8.3 inches wide, and 2 inches high. What is the volume in cubic inches of 2 boxes? Hint Which fmula could you use to solve the problem? How many boxes are you finding the volume f? 18 Hint Grace has a container in the shape of a cylinder to ste her candy. The height of the candy dish is 6 centimeters. If the volume of the container is cubic centimeters, what is the area of the base? What is the question asking you find? Are you already given the volume? What operation do you use to determine the area of the base when given the volume and the height? Hint The volume of the triangular prism below is 30 cubic units. What pieces of infmation do you have? What pieces are missing? 4 units What is the area of the base in square units?

12 7.5 Hint Gustavo made a ceramic container in the shape of a cylinder. The diagram below shows the dimensions of the container. 4 in. 12 in. What is the approximate volume in cubic inches of the container? What shape is the container? What fmula should you use f this three dimensional figure? What does the 12 in. represent in this problem? 415 The base of a triangular prism is shown below. Use your ruler to measure the base and height of the triangle to the nearest half centimeter. If the height of the triangular prism is 3.75 cm, determine the volume in cubic centimeters of the triangular prism A company developed a box in the shape of a triangular prism, as shown below. What is the volume of the box? 9 ft 2 ft Hint What unit of measure must you use on your ruler? Where are the base and height of the triangle? The height and base of a triangle are perpendicular to each other. What is the question asking you to determine? What infmation do you have? Hint What fmula should you use f this three-dimensional figure? The height of the prism connects the two bases. Start with determining the area of the triangle. 2 ft

13 Name: Evaluate: 1. The volume of a triangular prism is cubic inches. If the area of the base is 7.5 square inches, what is the height of the triangular prism? Recd your answer and fill in the bubbles. Be sure to use the crect place value. 2. Mr. Hemison is building a rectangular sandbox that is 1 2 feet high by 6 feet wide by feet long. If Mr. Stovall fills the box with sand, approximately how many cubic feet of sand will it take to fill the sandbox? A ft³ B ft³ C ft³ D ft³

14 3. Apollonia sketches the triangular prism, as shown below ft 5 ft 4 ft 6 ft What is the volume of the triangular prism? A B C 51 ft³ ft³ ft³ D 306 ft³ 4. In art class, Alexander designed a mug in the shape of a cylinder. The figure below shows the shape and size of the base of the mug. Use a ruler to measure the diameter of the mug to the nearest quarter inch. If the height of the mug is 4 inches, what is the volume of the mug? A B C 9.42 in.³ in.³ in.³ D in.³