Solid Figures Polyhedrons Prisms Pyramids Reteaching 8- Properties of polyhedrons include vertices, edges, and faces, and base(s). Square Pyramid K Reteaching 8- Not Polyhedrons Cylinder Cone Sphere H L I Vertices: H, I, J, K, L Edges: HI, IJ, JL, LH, HK, IK, JK, LK Faces: HIK, IJK, JKL, and HLK Base: HIJL Nets Identify solid figures from a net: a pattern that folds into the solid. J Cube Cylinder Classify the polyhedron. Name all vertices, edges, faces, and bases.. B A C E D G F H K I In through 4, classify each figure.. 3. 4. Topic 8
Solid Figures Classify the polyhedron. Name all vertices, edges, faces, and bases. Practice 8-. J L H K I M Practice 8- Classify each figure.. 3. 4. 5. Which solid figure looks like a round cake? 6. Number Sense How many faces make up six number cubes? 7. Reasoning A factory buys the boxes it needs in the form of flat nets. What advantages might the factory have in doing this? 8. What is the name of the polyhedron shown below? A Rectangular prism B Hexagonal prism C Pentagonal prism D Octagonal prism 9. Writing to Explain Describe the similarities and differences of a cylinder and a cone. Topic 8 3
Surface Area Reteaching 8- You can use formulas to find the surface area of different solid figures. Rectangular Prism Triangular Prism 5 in. 5 ft Reteaching 8-7 in. SA lw lh wh (5 7) (5 3) (7 3) 70 30 4 4 The surface area is 4 in. 3 ft 5 ft 4 ft SA ( _ 4 3) (3 5) (4 5) (5 5) 5 0 5 7 The surface area is 7 ft. Find the surface area of each figure.. 6 ft 0 ft 8 ft 5 ft. 9 in. 9 in. 9 in. Find the surface area of each rectangular prism. 3. l 5.5 cm, w 4.5 cm, h 3.5 cm 4. l 5 in., w 9 in., h 3.8 in. 5. l yd, w 6 yd, h.7 yd 6. Reasoning Write the dimensions of two different rectangular prisms that have the same surface area. 8 Topic 8
Surface Area Find the surface area of each figure... 3. Practice 8-6. cm 5.8 m in. 0 in. 0 in. 6. cm 6. cm. m 3.7 m Find the surface area of each rectangular prism. 4. l 6.9 mm, w 8. mm, h 4 mm Practice 8-5. l 3.4 cm, w.7 cm, h 6.5 cm 6. l 5.7 yd, w 9 yd, h.9 yd 7. Reasoning Margaret wants to cover a footrest in the shape of a rectangular prism with cotton fabric. The footrest is 8 in. in. 0 in. She has yd of fabric. Can she completely cover the footrest? 8. Which is the surface area of a rectangular prism with a length of., a width of. in., and a height of? A 6.48 in B 5.46 in C 4.58 in D.5 in 9. Writing to Explain A square pyramid has m sides on the base. Each face is a triangle with a base of m and a height of.5 m. Explain how to find the surface area. Topic 8 9
Volume of Rectangular Prisms Reteaching 8-3 Volume is the measure of space inside a solid figure. It is measured in cubic units. You can use a formula to find the volume of rectangular prisms: V 5 B 3 h where V stands for volume, B stands for the area of the base, and h stands for the height. To find the volume of the rectangular prism at the right, first find the area of the base. B 5 l 3 w 5 4 3 8 5 3 So the base is 3 sq in. Then use the volume formula to find the volume. V 5 B 3 h 5 3 3 5 5 60 So the volume is 60 sq in. Find the volume of each rectangular prism. Don t forget to label the units... 6 cm 4 in. 8 in. 5 in. in. Reteaching 8-3 3 cm 3 cm Area of Base (B 5 l 3 w): Volume (V 5 B 3 h): 5 in. in. Area of Base (B 5 l 3 w): Volume (V 5 B 3 h): 3. 4. 6 ft 9 m 0 ft 4 ft Area of Base (B 5 l 3 w): Volume (V 5 B 3 h): 5 m m Area of Base (B 5 l 3 w): Volume (V 5 B 3 h): 5. Find the volume of Rectangular Prism. How can you find the volume of Rectangular Prism without using the volume formula? 4 cm 8 cm cm 4 cm 8 cm cm Rectangular Prism Rectangular Prism Topic 8 35
Volume of Rectangular Prisms Find the volume of each rectangular prism.. 5 in. cm. 3. 6 in. 4 cm 9 cm 4 m Practice 8-3 4 m 4 m Practice 8-3 Find the missing value for each rectangular prism. 4. Volume = 6 cu in. 5. Volume = 96 cu yd 6. Volume = 5 cu ft Length = Length = Length = 5 ft Width = in. Width = 6 yd Width = Height = Height = 8 yd Height = 5 ft 7. Number Sense Suppose a box has a volume of cu yd. What is its volume in cubic feet? 8. A rectangular prism has a base of cm, a length of 3 cm, a width of 4 cm, and a height of 0 cm. Which is the volume of the prism? A 36 cm 3 B 48 cm 3 C 0 cm 3 D,440 cm 3 9. Writing to Explain Find and compare the volumes of the two rectangular prisms below. How does doubling the measure of each dimension in a rectangular prism change the volume of the prism? Length Width Height Volume Rectangular Prism 5 ft ft 0 ft Rectangular Prism 0 ft 4 ft 0 ft 36 Topic 8
Volume with Fractional Edge Lengths Reteaching 8-4 When finding the volume of a rectangular prism with fractional edge lengths, you have to find the number of cubes with fractional edge lengths that can fill the prism. What is the volume of the rectangular prism shown below at the right? Consider a _ -inch cube. 8 half-inch cubes can fill a -inch cube. Next, figure out how many _ -inch cubes will fill the prism. The prism can be filled with 5 7 3 05 half-inch cubes. Divide 05 by 8 because 8 half-inch cubes make up a -inch cube. 05 8 3 _ 8 The volume of this rectangular prism is 3 _ 8 in3. in. in. For through 4, find the volume of each rectangular prism.. in. 0 in.. 4 in. in. 3 in. 4 Reteaching 8-4 Fraction cubes have in. lengths. Fraction cubes have in. lengths. V V 3. 3.7 cm 4..5 m 4.5 cm 7. m 7. m. cm V V 5. Writing to Explain How many _ -inch cubes could fit inside the rectangular prism shown in Exercise? Explain how you know. Topic 8 4
Volume with Fractional Edge Lengths Find the volume of each rectangular prism... 3. ft 7 ft 4 ft 3.7 cm 0 cm 4. cm Practice 8-4 Practice 8-4 Find the missing value for each rectangular prism. 4. Volume: 3_ 8 in3 5. Volume: 8 _ 3 ft3 6. Volume: 758.6 mm 3 Base: 0 _ 4 in Length: Length: 3 mm Height: Width: 4 _ ft 3 Width: Height: _ ft 3 Height: 7. mm 7. Number Sense A rectangular prism can be filled with 0 half-inch cubes. How many _ -inch cubes would it take to fill the same prism? 4 8. A rectangular prism has a base with an area of 3.5 cm and a height of 4.7 cm. What is the volume of the prism? A 36. cm 3 C 48.05 cm 3 B 7.4 cm 3 D 96. cm 3 9. Writing to Explain Find and compare the volumes of the two rectangular prisms below. How does dividing each dimension of the larger prism by affect the volume of the smaller prism? Length Width Height Volume 5 in. 4 _ in. 6 in. _ in. _ in. 4 4 Topic 8