Grade 6 Area and Volume

Transcription

1 Name: lass: _ ate: _ I: Grade 6 rea and Volume Multiple hoice Identify the choice that best completes the statement or answers the question. 1. drama teacher is creating a scale model of the school s performing arts stage so that he can plan where to position props and actors in a play. What is the area of the scale model of the stage in square units? a. 14 square units c. 45 square units b. 28 square units d. 81 square units 2. construction company is preparing to pour a cement slab. The dimensions need to be 90.5 centimeters long, 30.5 centimeters wide, and 15.0 centimeters deep. Find the volume of cement needed to complete the job. a. 136 cm 3 c cm 3 b cm 3 d. 41, cm 3 1

2 Name: I: 3. Find the surface area of the rectangular prism. a. 612 cm 2 c. 588 cm 2 b. 306 cm 2 d. 534 cm 2 4. The base of the triangular prism has how many edges? a. 3 c. 6 b. 2 d single edge of the base of the cube is parallel to how many other edges? a. 13 c. 4 b. 12 d. 3 2

3 Name: I: 6. hris s mother is making stars for the holiday displays at the store where she works. The stars are made out of square pieces of construction paper measuring 30 inches on each side. What is the area of the star figure below? a. 300 square inches c. 500 square inches b. 60 square inches d. 200 square inches 7. Neva makes a 2-dimensional representation of a spool of thread. The height of the spool is 22 inches. The middle part of the spool where the thread is wound is a square with 5-inch sides. The top and the bottom of the spool are congruent isosceles trapezoids. What is the height of the top of the spool? a. 17 inches c. 6 inches b. 7.5 inches d. 8.5 inches 3

4 Name: I: 8. This is an outline of the drian s house with the dimensions shown in feet. rea of a rectangle = length width rea of a square = side side What is the area of the drian s house? a. 2,800 square feet c. 2,430 square feet b. 2,754 square feet d. 5,184 square feet 9. Which of the following shapes is a rectangular pyramid? a. c. b. d. 4

5 Name: I: 10. Which of the following shapes is a triangular pyramid? a. c. b. d. 11. Which of these is a rectangular prism? a. c. b. d. 12. Which of these is a triangular prism? a. c. b. d. 5

6 I: Grade 6 rea and Volume nswer Section MULTIPLE HOIE 1. NS: The dimensions of the model are 9 units by 5 units. Multiply these two numbers to find the area of the rectangular stage. 9 5 = 45 What is the formula for the area of a rectangle? Is this the area or the perimeter of the stage? What are the dimensions of the stage in linear units? PTS: 1 IF: loom s Level: pplication Webb s Level: Level 1 REF: The rts OJ: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. NT: 6: 6.G.1 ST: 6: 6.G.1 TOP: Geometry KEY: coordinates area rectangle I: M NS: The volume of a rectangular prism can be found by multiplying the length by the width by the height. V = lwh V = 90.5 cm 30.5 cm 15.0 cm V = 41, cm 3 To find the volume of the prism, you will need to multiply. What is the formula for finding the volume of a prism? id you include all measurements in the formula for volume? PTS: 1 IF: loom s Level: pplication Webb s Level: Level 2 REF: Workplace OJ: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. pply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. NT: 6: 6.G.2 ST: 6: 6.G.2 TOP: Geometry KEY: volume rectangular prism I: M

7 I: 3. NS: The surface area of a rectangular prism is the sum of the 6 surface areas that make up the prism. Use the length of each side to find the surface area. S = 2ab + 2ac + 2bc S = 2( 12 cm) ( 13 cm) + 2( 12 cm) ( 6 cm) + 2( 13 cm) ( 6 cm) Ê S = cm 2 ˆ Ê ˆ Ê ˆ ËÁ cm2 ËÁ cm2 ËÁ S = 312 cm cm cm 2 S = 612 cm 2 Find the area of each rectangle and add them together. Remember to include all 6 rectangles in the calculation. onsider the formula for the surface area of a rectangular prism. arefully look at the net to determine the length of each side of each rectangle. id you remember to include all sides of the cube in your calculation? PTS: 1 IF: loom s Level: nalysis Webb s Level: Level 2 OJ: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. pply these techniques in the context of solving real-world and mathematical problems. NT: 6: 6.G.4 ST: 6: 6.G.4 TOP: Geometry KEY: surface area 3-dimensional net rectangular prism I: M NS: n edge is the place where the base and another face meet. The base of the triangular prism has 3 edges. ouble check your work by counting the number of faces that touch the base. Remember that an edge is the place where two faces meet. How many edges touch the base? This is the total number of faces for a triangular prism. PTS: 1 IF: loom s Level: nalysis Webb s Level: Level 1 OJ: nalyze characteristics and properties of three-dimensional geometric shapes and use visualization and spatial reasoning to recognize shapes. Identify relationships in three-dimensional shapes (faces, vertices, edges, parallel, perpendicular, intersecting). NT: NO LIGNMENT FOUN ST: NO LIGNMENT FOUN TOP: Geometry KEY: geometric shapes 3-dimensional shapes base edge I: M

8 I: 5. NS: Parallel edges are two or more edges that will not intersect. There are 3 parallel edges to a single edge of the base of a cube. Parallel edges will not intersect at any point. Look at the cube again to determine the number of parallel edges. This is the total number of edges for a cube. re you sure you counted correctly? PTS: 1 IF: loom s Level: nalysis Webb s Level: Level 1 OJ: nalyze characteristics and properties of three-dimensional geometric shapes and use visualization and spatial reasoning to recognize shapes. Identify relationships in three-dimensional shapes (faces, vertices, edges, parallel, perpendicular, intersecting). NT: NO LIGNMENT FOUN ST: NO LIGNMENT FOUN TOP: Geometry KEY: geometric shapes 3-dimensional shapes parallel edge I: M

9 I: 6. NS: The star is made up of four congruent triangles and a small square. Each of the congruent triangles has a base the length of the small square and height the length of the small square. small square has side: 30 inches 3 = 10 inches. This means that for each triangle: b = 10 inches and h = 10 inches. Thus, the area of each triangle is: Triangle = 1 2 b h = inches 10 inches = 50 square inches. The area of the small square is: Small Square = a 2 = 10 inches 10 inches = 100 square inches. The total area of the star is: Star = 4 Triangle + Square = = 300 square inches. You need to calculate the area of the triangles and small square in square inches. The four triangles are congruent with height = base. The small square has twice the area of a triangle. PTS: 1 IF: loom s Level: pplication Webb s Level: Level 1 REF: Workplace OJ: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. NT: 6: 6.G.1 ST: 6: 6.G.1 TOP: Geometry KEY: geometric properties symmetry congruent triangles area triangle square I: M

10 I: 7. NS: ecause of symmetry, the height of two trapezoids is the total height of the spool minus the height of the threaded part (see picture below). So: height of 2 trapezoids = 22 inches 5 inches or 17 inches. The height h of one trapezoid is half of this number: h = inches = 8.5 inches. This is the height of two trapezoid panes. You made a mistake in your arithmetic. Subtract the side length of the center square from the total height of the spool. PTS: 1 IF: loom s Level: pplication Webb s Level: Level 1 REF: The rts OJ: Represents and applies geometric properties and relationships to solve real-world and mathematical problems. NT: NO LIGNMENT FOUN ST: NO LIGNMENT FOUN TOP: Geometry KEY: geometric properties congruent figures symmetry reflections I: M

11 I: 8. NS: Notice that the house consists of two squares. One square is 27 feet per side, and the other square is 45 feet per side. The area of the first square is 27 2 = ( 27 27) = 729 square feet. The area of the second square is 45 2 = ( 45 45) = 2,025 square feet. The area of the whole house is ,025 = 2,754 square feet. Is your answer exact, or did you round it? id you notice that the house consists of two squares? alculate the area of one square at a time. Figure out the areas of each square, then add them together. PTS: 1 IF: loom s Level: pplication Webb s Level: Level 1 OJ: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. NT: 6: 6.G.1 ST: 6: 6.G.1 TOP: Geometry KEY: area squares I: M NS: rectangular pyramid has one rectangular base and four triangular faces. This is a rectangular prism. This is a triangular pyramid. This is a triangular prism. PTS: 1 IF: loom s Level: Knowledge Webb s Level: Level 1 OJ: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. pply these techniques in the context of solving real-world and mathematical problems. NT: 6: 6.G.4 ST: 6: 6.G.4 TOP: Geometry KEY: shapes identify rectangular pyramid 3-dimensional I: M

12 I: 10. NS: triangular pyramid has four triangular faces. This is a rectangular prism. This is a triangular prism. This is a rectangular pyramid. PTS: 1 IF: loom s Level: Knowledge Webb s Level: Level 1 OJ: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. pply these techniques in the context of solving real-world and mathematical problems. NT: 6: 6.G.4 ST: 6: 6.G.4 TOP: Geometry KEY: shapes identify triangular pyramid 3-dimensional I: M NS: rectangular prism has six rectangular faces. This is a rectangular pyramid. This is a triangular prism. This is a triangular pyramid. PTS: 1 IF: loom s Level: Knowledge Webb s Level: Level 1 OJ: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. pply these techniques in the context of solving real-world and mathematical problems. NT: 6: 6.G.4 ST: 6: 6.G.4 TOP: Geometry KEY: shapes identify triangular pyramid 3-dimensional I: M NS: triangular prism has three rectangular faces and two triangular bases. This is a rectangular pyramid. This is a triangular pyramid. This is a rectangular prism. PTS: 1 IF: loom s Level: Knowledge Webb s Level: Level 1 OJ: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. pply these techniques in the context of solving real-world and mathematical problems. NT: 6: 6.G.4 ST: 6: 6.G.4 TOP: Geometry KEY: shapes 3-dimensional identify triangular pyramid I: M