Module 4: Prisms and Cylinders PDF

# MODULE 4: Les prismes et les cylindres ## Amuse-toi! Serrons-nous la main **Instructions:** - Draw a circle and represent people with points. - Connect each point to all other points to represent handshakes. - Record results in the table. - Describe the pattern in the number of handshakes. |...

# MODULE 4: Les prismes et les cylindres ## Amuse-toi! Serrons-nous la main **Instructions:** - Draw a circle and represent people with points. - Connect each point to all other points to represent handshakes. - Record results in the table. - Describe the pattern in the number of handshakes. | Nombre de personnes | Nombre de poignées de main | |---|---| | 1 | 0 | | 2 | 1 | | 3 | 3 | | 4 | | | 5 | | | 6 | | | 7 | | ## La chasse aux mots **Instructions:** - Find the words from the list in the following grid: - Words can be horizontal, vertical, or diagonal. - Write the 12 unused letters in order, by row, from left to right, separated by spaces. - Create a sentence from the unused letters. **Word list:** - ANGLE - AIRE - BASE - BOÎTE - CAPACITÉ - CUBE - DÉCAGONE - QUATRE - HEXAGONE - MÈTRE - PRISME - PYRAMIDE - RECTANGLE - CARRÉ - DEUX **Grid:** ``` EBASEEVIEP MLVETLRNEY SSGMIAOTTR IHSNCGSREA RHEXAGONEM PVTCPTMCRI XUEDARCAID DDSBCUBEA E ERTAUQDPRT ETIOBANGLE ``` ## Rappelle-toi! L'aire des figures à deux dimensions **Instructions:** - Calculate the area of each triangle. - Calculate the area of each triangle. **Triangle:** - Base: 7.8 cm - Height: 1.8 cm - Area: $A = \frac{bh}{2} = \frac{1}{2} * 7.8 * 1.8 = 7.02$ cm² **Triangles:** **a)** - Base: 7 m - Height: 12 m - Area: $A = \frac{bh}{2}$ = __ m² **b)** - Base: 3.4 cm - Height: 5.6 cm - Area: $A = \frac{bh}{2}$ = __ **Triangles:** **a)** - Base: 3.5 cm - Height: 6.4 cm - Area: A = ___ **b)** - Base: 8.6 cm - Height: 4.2 cm - Area: A = ___ **Circle:** - Diameter: 14 cm - Radius: 7 cm - Area: $A = πr² = π * 7² ≈ 153.938 cm²$ ≅ 154 cm² **Circle:** - Calculate the area of each circle and round to the nearest whole number. **a)** - Diameter: 24 cm - Radius: __ cm - Area: A = __ cm² **b)** - Radius: 9 m - Area: A = __ m² **c)** - Diameter: 11 mm - Area: A = __ mm² **d)** - Radius: 8 km - Area: A = __ km² **Circumference of a circle** - Calculate the circumference of a circle with a diameter of 4.8 cm: - Circumference: $C = πd = π * 4.8 ≈ 15.080$ cm ≅ 15.1 cm - Calculate the circumference of a circle with a radius of 5.2 cm: - Circumference: $C = 2πr = 2 * π * 5.2 ≈ 32.673$ cm ≅ 32.7 cm **Circle** - Calculate the circumference of each circle and round to one decimal place. **a)** - Diameter: 12 cm - Circumference: C = π * d ≈ __ cm **b)** - Radius: 8 m - Circumference: C = 2 * π * r ≈ __ m **c)** - Diameter: 5.6 mm - Circumference: C = __ mm **d)** - Radius: 3.8 m - Circumference: C = __ m # 4.1 Les développements ## Révision éclair - A **prism** has congruent bases, and its name is based on its bases. - A **pyramid** has one base, with all other faces being congruent triangles. - A **net** is a diagram that can be folded to create a solid shape. ## À ton tour **1.** Draw a net of a rectangular prism, labeling each face. **Dimensions:** - Length: 6 cm - Width: 2 cm - Height: 3 cm **2.** Draw a net of a triangular prism, labeling each face. **Dimensions:** - Base length: 5 m - Base height: 6 m - Height: 7 m **3.** Which of the following nets does not represent a cube? **a, b, and c** are each diagrams representing nets. **4. a)** Match each object with its net. **a, b, c, d, e, and f** are each diagrams representing objects and nets. **b)** Label all faces of each object. **5.** For each description, name a shape with the given faces: **a)** Six congruent triangles and a hexagon **b)** Four congruent equilateral triangles **c)** Two congruent squares and four congruent rectangles **d)** Two congruent triangles and three rectangles # 4.2 Construire des objets à partir de développements ## Révision éclair - To determine if a net represents a solid shape, examine each face and how it would be arranged. - The diagram below represents the net of square-based pyramid. **A** and **B** are labeled on the diagram. > The net shown does not represent a square-based pyramid. If the net were folded, triangles **A** and **B** would overlap. ## À ton tour **1.** Which of these nets does not represent a cylinder? **a, b, and c** are each diagrams representing nets **Dimensions:** - Diameter: 11 cm - Height: 5 cm ## 2.** Does each of the following nets represent a solid shape? - If yes, name the object and describe it. - If not, explain what modifications are required to create a net. **a, b, and c** are each diagrams representing nets. ## 3.** Name and describe the object represented by the following net. **The net is a diagram representing a solid shape.** ## 4.** Name the object represented by each of these nets. **a, b, and c** are each diagrams representing nets. ## 5.** Describe how to modify each of the following nets to create a net of a solid shape. Name the object represented by the new net. **a, b, and c** are each diagrams representing nets. **Dimensions:** - **a**: 13 cm, 12 cm, 5 cm - **b**: 5 cm, 12 cm, 5 cm - **c**: 5 m, 12 m # 4.3 L'aire de la surface d'un prisme droit à base rectangulaire ## Révision éclair - The ***total surface area*** of a rectangular prism is the sum of the areas of all its rectangular faces. It equals the area of the net. - In the diagram below, each rectangle is labeled. **Dimensions:** - Length: 4 cm - Width: 3 cm - Height: 5 cm **Calculations:** **A:** - Area: 3 cm * 5 cm = 15 cm² **B:** - Area: 4 cm * 3 cm = 12 cm² **C:** - Area: 4 cm * 5 cm = 20 cm² **Total Surface Area:** - 2 * 15 cm² + 2 * 12 cm² + 2 * 20 cm² = 94 cm² ## À ton tour **1.** Calculate the surface area of the rectangular prism represented by its net. **The net represents a prism with the surface area of each face labeled.** **Dimensions:** - Length: 12 cm - Width: 12 cm - Height: 8 cm **Total surface Area:** 2 * __ cm² + 2 * __ cm² + 2 * __ cm² = __ cm² ## 2.** Calculate the total surface area of the rectangular prism. **The diagram is a representation of the prism.** **Dimensions:** - Length: 8 m - Width: 5 m - Height: 1 m **Calculations:** - **A:** __*__ = __ - **B:** __*__ = __ - **C:** __*__ = __ **Total surface Area:** 2 * __ + 2 * __ + 2 * __ = __ ## 3.** Glenda and Louis are each designing a rectangular box. Whose design has the larger total surface area? Show all your calculations. **Glenda’s Design:** **Dimensions:** - Length: 12 cm - Width: 8 cm - Height: 20 cm **Calculations:** **A:** __ + __ + __ = __ **Louis’ Design:** **Dimensions:** - Length: 24 cm - Width: 6 cm - Height: 10 cm **Calculations:** **A:** __ + __ + __ = __ **Answer:** The box designed by __ has the larger surface area. ## 4.** The surface area of a cube is 294 cm². **a)** What is the area of each face of the cube? **Calculations:** - Area of each face: __ **b)** What is the edge length of the cube? **Calculations:** - Edge length: __ ## 5.** An office building that resembles a rectangular prism is 200 m tall, 60 m long, and 40 m wide. The top quarter of each vertical face will be covered in a large banner. What is the total area of the banner? **Calculations:** **Surface area of the Banner:** - (1/4) * __ * __ + (1/4) * __ * __ + (1/4) * __ * __ + (1/4) * __ * __ = __ m² # 4.4 L'aire de la surface d'un prisme droit à base triangulaire ## Révision éclair - To calculate the surface area of a triangular prism, determine the area of each face and add them. **Dimensions:** - Base: 14 cm - Height: 4 cm - Length: 7 cm **Calculations:** **A:** 8 cm * 7 cm = 56 cm² **B:** 14 cm * 7 cm = 98 cm² **C:** 8 cm * 7 cm = 56 cm² **D:** 1/2 * 14 cm * 4 cm = 28 cm² **E:** 1/2 * 14 cm * 4 cm = 28 cm² **Total Surface Area:** 56 cm² + 98 cm² + 56 cm² + 28 cm² + 28 cm² = 266 cm² ## À ton tour **1.** Calculate the surface area of the triangular prism represented by its net. **Dimensions:** - Base: 3 m - Height: 4 m - Length: 5 m **Calculations:** **A:** __ * __ = __ **B:** __ * __ = __ **C:** __ * __ = __ **D:** 1/2 * __ * __ = __ **E:** 1/2 * __ * __ = __ **Total Surface Area:** __ + __ + __ + __ + __ = __ m² ## 2.** Determine the total surface area of each prism below. **a)** - Base: 5 cm - Height: 4 cm - Length: 6 cm - Total Surface Area: 5 cm * 6 cm + 5 cm * 11 cm + 4 cm * 6 cm + 2 * (1/2 * 4 cm * 5 cm) = __ cm² **b)** - Base: 5 m - Height: 10 m - Length: 12 m - Total Surface Area: 5 m * 12 m + 10 m * 12 m + 5 m * 13 m + 2 * (1/2 * 10 m * 5 m) = __ m² **c)** - Base: 5 m - Height: 7 m - Length: 7 m - Total Surface Area: 5 m * 7 m + 5 m * 8 m + 7 m * 7 m + 2 * (1/2 * 7 m * 5 m) = __ m² **d)** - Base: 5.7 m - Height: 9 m - Length: 7 m - Total Surface Area: 5.7 m * 7 m + 5.7 m * 9 m + 7 m * 4 m + 2 * (1/2 * 5.7 m * 4 m) = __ m² ## 3.** Determine the surface area of the triangular prism. **Dimensions:** - Base: 6 cm - Height: 16 cm - Length: 10 cm **Calculations:** **Surface Area:** 2 * (1/2 * 6 cm * 16 cm) + 6 cm * 10 cm + 16 cm * 10 cm + 28 cm * 10 cm = __ cm² ## 4.** Determine the area of the net of a prism. **Dimensions:** - Base: 12 cm - Height: 13 cm - Length: 5 cm **Calculations:** - Area of net: 5 cm * 13 cm + 5 cm * 12 cm + 13 cm * 12 cm + 2 * (1/2 * 12 cm * 13 cm) = __ cm² ## 5.** Calculate the total surface area of the prism. **Dimensions:** - Base: 4 mm - Height: 3 mm - Length: 5 mm - Depth: 18 mm **Calculations:** - Total Surface Area: 18 mm * 5 mm + 18 mm * 4 mm + 4 mm * 5 mm + 2 * (1 / 2 * 4 mm * 3 mm) + 2 * (1/2 * 3 mm * 5 mm) = __ mm² # 4.5 Le volume d'un prisme droit à base rectangulaire ## Révision éclair - To find the volume of a rectangular prism, multiply the area of its base by its height. **Dimensions:** - Length: 10 cm - Width: 4 cm - Height: 8 cm **Calculations:** - Area of the base: 10 cm * 4 cm = 40 cm² - Volume: - V = Bh = 40 cm² * 8 cm = 320 cm³ ## À ton tour **1.** Determine the volume of each rectangular prism. **a.** - Base area: 60 cm² - Height: 8 cm - Volume: V = Ah = 60 cm² * 8 cm = __ cm³ **b**. - Base area: 36 cm² - Height: 6 cm - Volume: V = Ah = __ cm³ **c.** - Base area: 12 m² - Height: 9 m - Volume: V = Ah = __ cm³ ## 2.** Determine the volume of each prism. **a.** - Length: 8.5 m - Width: 7 m - Height: 6 m **Calculations:** - Area of the base: __ * __ = __ m² - Volume: V = Ah = __ m² * __ m = __ m³ **b.** - Length: 4.8 cm - Width: 3 cm - Height: 10.5 cm **Calculations:** - Area of the base: __ * __ = __ cm² - Volume: V = Ah = __ cm² * __ cm = __ cm³ **c.** - Length: 3.5 mm - Width: 5.5 mm - Height: 4 mm **Calculations:** - Area of the base: __ * __ = __ mm² - Volume: V = Ah = __ mm² * __ mm = __ mm³ ## 3.** A rectangular prism is 16 cm long, 12 cm wide, and 5 cm high. **a.** What is the volume of the prism? **Calculations:** - Volume: __ * __ * __ = __ cm³ **b.** What is the new volume if the length is halved and the height is doubled? **Calculations:** - New length: __ cm - New height: __ cm - New volume: __ cm * __ cm * __ cm ## 4.** Which of these rectangular prisms has a larger volume? **A.** Length: 6 m, Width: 4.5 m, Height: 3.6 m **B.** A cube that is 4.6 m on each edge. **Calculations:** **A.** Volume: __ * __ * __ = __ m³ **B.** Volume: __ * __ * __ = __ m³ - The prism with the greater volume is __. - The difference between the volumes of the two prisms is __ m³. ## 5.** A fish pond shaped like a rectangular prism is 4 m long, 3 m wide, and 2 m deep. **a.** What is the volume of the empty pond? **Calculations:** - Volume of the pond: __ * __ * __ = __ m³ **b.** If the pond is filled to a depth of 1.5 m, what is the volume of water in the pond, in liters? (Remember that 1 L = 1000 cm³.) **Calculations:** - Volume of water: __ m * __ m * __ m = __ m³ **Conversions:** - Length: __ m = __ cm - Width: __ m = __ cm - Depth: __ m = __ cm - Volume of water: __ cm * __ cm * __ cm = __ cm³ = __ L # 4.6 Le volume d'un prisme droit à base triangulaire ## Révision éclair - To find the volume of a triangular prism, first find the area of its triangular base and then multiply it by the prism’s length, l. **Dimensions:** - Base: 9 cm - Height: 5 cm - Length: 12 cm **Calculations:** - Area of the triangle: 1/2 * 9 cm * 5 cm = 22.5 cm² - Volume: - V = Al = 22.5 cm² * 12 cm = 270 cm³ ## À ton tour **1.** Determine the volume of each triangular prism. **a**. - Base area: 5 m² - Length: 12 m - Volume: V = Al = __ m² * __ m = __ m³ **b**. - Base area: 14 cm² - Length: 20 cm - Volume: V = Al = __ cm² * __ cm = __ cm³ ## 2.** Determine the volume of each prism. **a.** - Base: 7 cm - Height: 4 cm - Length: 12 cm **Calculations:** - Area of triangle: 1/2 * 7 cm * 4 cm = __ cm² - Volume: V = Al = __ cm² * 12 cm = __ cm³ **b.** - Base: - length: 6 m - height: 2 m - Length: 5 m - Volume: V = Al = __ m² * __ m = __ m³ **c.** - Base: - length: 2 mm - height: 1.5 mm - Length: 3.8 mm - Volume: V = Al = __ mm² * __ mm = __ mm³ ## 3.** The volume of a triangular prism is 27.8 cm³. The prism is 5 cm long. What is the area of each triangular base? **Calculations:** - Area of the base: A = V/l = 27.8 cm³ / 5 cm = __ cm² ## 4.** The volume of a triangular prism is 6 cm³. Determine all possible whole number values for the area, *A*, of the base and the length, *l*, of the prism. Create a table to display your results. | A | l | |---|---| | | | ## 5.** Determine the volume of the prism. **Dimensions:** - Base: 6 cm - Height: 10 cm - Depth: 9 cm **Calculations:** - Area of the base: 1/2 * 6 cm * 10 cm = __ cm² - Volume: V = Al = __ cm² * 9 cm = __ cm³ ## 6.** a) Determine the volume of the prism. **Dimensions:** - Base: 15 cm - Height: 20 cm - Length: 10 cm **Calculations:** - Area of the base: 1/2 * 15 cm * 20 cm = __ cm² - Volume: V = Al = __ cm² * 10 cm = __ cm³ **b.** Suppose the prism contains 1200 mL of water. What is the depth of the water? (Remember 1 cm³ = 1 mL) **Calculations:** - V = 1200 mL = __ cm³ - A = 1/2 * 15 cm * 20 cm = __ cm² - l = V/A = __ cm³ / __ cm² = __ cm - Depth: __ cm # 4.7 L'aire de la surface d'un cylindre droit ## Révision éclair - To find the total surface area of a cylinder, add the area of its two circular bases to the area of its rectangular lateral surface. **Dimensions:** - Radius: r = 6 cm - Height: h = 5 cm **Calculations:** - Area of one circle: $πr² = π * 6² ≈ 113.10 cm² $ - Area of the rectangle: $2πr * h = 2 * π * 6 * 5 ≈ 188.50 cm² $ - Total surface area: 2 * 113.10 cm² + 188.50 cm² = 414.70 cm² ≈ 415 cm² ## À ton tour **1.** Determine the surface area of each cylinder to the nearest square centimeter. **a.** - Radius: 4 cm - Height: 12 cm **Calculations:** - Area of one circle: $ πr² = π * 4² ≈ 50.27 cm² $ - Area of the rectangle: $2πr * h = 2 * π * 4 * 12 ≈ 301.59 cm² $ - Total surface area: 2 * 50.27 cm² + 301.59 cm² = __ cm² ≈ __ cm² **b.** - Diameter: 8 cm - Height: 20 cm **Calculations:** - Radius: 4 cm - Area of one circle: $πr² = π * 4² ≈ 50.27 cm² $ - Area of the rectangle: $2πr * h = 2 * π * 4 * 20 ≈ 502.65 cm² $ - Total surface area: 2 * 50.27 cm² + 502.65 cm² = __ cm² ≈ __ cm² **c.** - Base: 2 cm - Height: 16 cm **Calculations:** - Radius: __ cm - Area of one circle: $πr² = π * __² ≈ __ cm² $ - Area of the rectangle: $2πr * h = 2 * π * __ * 16 ≈ __ cm² $ - Total surface area: 2 * __ cm² + __ cm² = __ cm² ≈ __ cm² ## 2.** Determine the total surface area of each cylinder to the nearest whole number. **a.** - Radius: 8 cm - Height: 12 cm **Calculations:** - Area of one circle: $πr² = π * 8² ≈ 201.06 cm² $ - Area of the rectangle: $2πr * h = 2 * π * 8 * 12 ≈ 603.19 cm² $ - Total surface area: 2 * 201.06 cm² + 603.19 cm² = __ cm² ≈ __ cm² **b.** - Diameter: 9 m - Height: 6.8 m **Calculations:** - Radius: __ m - Area of one circle: $πr² = π * __² ≈ __ m² $ - Area of the rectangle: $2πr * h = 2 * π * __ * 6.8 ≈ __ m² $ - Total surface area: 2 * __ m² + __ m² = __ m² ≈ __ m² **c.** - Diameter: 7.2 cm - Height: 9.3 cm **Calculations:** - Radius: __ cm - Area of one circle: $πr² = π * __² ≈ __ cm² $ - Area of the rectangle: $2πr * h = 2 * π * __ * 9.3 ≈ __ cm² $ - Total surface area: 2 * __ cm² + __ cm² = __ cm² ≈ __ cm² ## 3.** Determine the surface area of each cylinder rounded to one decimal place. The cylinders are open at one end. **a.** - Diameter: 15 m - Height: 7 m **Calculations:** - Radius: __ m - Area of the circle: $πr² = π * __² ≈ __ m² $ - Area of the rectangle: $2πr * h = 2 * π * __ * 7 ≈ __ m² $ - Total surface area: __ m² + __ m² ≈ __ m² **b.** - Diameter: 23 cm - Height: 4.8 cm **Calculations:** - Radius: __ cm - Area of the circle: $πr² = π * __² ≈ __ cm² $ - Area of the rectangle: $2πr * h = 2 * π * __ * 4.8 ≈ __ cm² $ - Total surface area: __ cm² + __ cm² ≈ __ cm² ## 4.** A steel mill uses cylindrical rollers. One roller is 1.8 m in diameter and 2.6 m long. What is the surface area of the curved portion of the roller? **Calculations:** - Radius: __ m - Area of the curved portion: $2πrh = 2 * π * __ * 2.6 ≈ __ m² $ ## 5.** The total surface area of an open cylinder is 377 cm². The height of the cylinder is 10 cm. **a.** What is the circumference of the base of the cylinder? **Calculations:** - Area of the curved portion: __ cm² - Circumference * height = Area of curved portion - Circumference * __ cm = __ cm² - Circumference = __ cm² / __ cm = __ cm **b.** What is the radius of the base of the cylinder? **Calculations:** - Circumference: $2πr = __ cm$ - $r = 2π / __ cm ≈ __ cm$ # 4.8 Le volume d'un cylindre droit ## Révision éclair - To find the volume of a cylinder, multiply the area of its base by its height. **Dimensions:** - Base area: 312 m² - Height: 9 m **Calculations:** - Volume: 312 m² * 9 m = 2808 m³ **Dimensions:** - Diameter: 18 cm - Height: 15 cm **Calculations:** - Radius: 9 cm - Volume: V = πr²h ≈ 3.14 * 9² * 15 ≈ 3817 cm³ ## À ton tour **1.** Determine the volume of each cylinder rounded to the nearest whole number. The areas of the bases and heights are given. **a.** - Base area: 27.6 cm² - Height: 4 cm - Volume: __ cm² * __ cm = __cm³ ≈ __ cm³ **b.** - Base area: 423 cm² - Height: 9 cm - Volume: __ cm² * __ cm = __cm³ ≈ __ cm³ **c.** - Base area: 75.8 m² - Height: 63 m - Volume: __ m² * __ m = __m³ ≈ __ m³ ##2.** Determine the volume of each cylinder to the nearest whole number. **a.** - Radius: 6 cm - Height: 9 cm **Calculations:** - Volume: V = πr²h ≈ 3.14 * 6² * 9 ≈ __ cm³ **b.** - Diameter: 18 mm - Height: 35 mm **Calculations:** - Radius: __ mm - Volume: V ≈ 3.14 * __² * __ mm ≈ __ mm³ **c.** - Diameter: 9 m - Height: 12 m **Calculations:** - Radius: __ m - Volume: V ≈ 3.14 * __² * __ m ≈ __ m³ ## 3.** Determine the volume of each cylinder to one decimal place. **a.** - Radius: 12 cm - Height: 12 cm **Calculations:** - Volume: V ≈ 3.14 * 12² * 12 ≈ __ cm³ **b**. - Diameter: 16.8 m - Height: 5.4 m **Calculations:** - Radius: __ m - Volume: V ≈ 3.14 * __² * 5.4 ≈ __ m³ ## 4.** Based on their volumes, which cylinder is larger? By how much? **A.** Radius: 6.4 cm, Height: 3.2 cm **B.** Radius: 4.3 cm, Height: 7.2 cm **Calculations:** **A.** Volume: V ≈ 3.14 * 6.4² * 3.2 ≈ __ cm³ **B.** Volume: V ≈ 3.14 * 4.3² * 7.2 ≈ __ cm³ - The cylinder that is larger is __. - The difference in volume between the two cylinders is __ cm³. ## 5.** a) Determine, to one decimal place, the volume of a cylinder that has a radius of 5 cm and a height of 10 cm. **Calculations:** - Volume: V ≈ 3.14 * 5² * 10 ≈ __ cm³ **b.** What happens to the volume of the cylinder in part **a)** if the radius is doubled? - Doubling the radius results in a volume that is __ times the original volume. **c.** What happens to the volume of the cylinder in part **a)** if the height is doubled? - Doubling the height results in a volume that is __ times the original volume. # Dans tes propres mots - Create a glossary of terms, including definitions and examples. | Terme | Définition | Exemple | |---|---|---| | Développement | Une figure ou un schéma qui peut être plié pour créer un objet. | Le schéma d'un cube qui peut être plié pour former un cube. | | Polyèdre | Un solide géométrique dont les faces sont des polygones. | Un cube, un prisme, une pyramide. | | Prisme régulier | Un prisme dont les faces latérales sont des rectangles identiques et dont les bases sont des polygones réguliers identiques. | Un prisme à base carrée. | | Pyramide régulière | Une pyramide dont la base est un polygone régulier et dont toutes les arêtes latérales ont la même longueur. | Une pyramide à base carrée. | | Aire de la surface ou aire totale | La somme des aires de toutes les faces d'un solide. | L'aire totale d'un cube est la somme des aires de ses 6 faces carrées. | | Volume | La quantité d'espace qu'occupe un solide. | Le volume d'un cube est la mesure de l'espace qu'il occupe. | ## Énumère d'autres termes mathématiques que tu dois connaître. - Arêtes - Sommets - Faces - Base - Côté - Hauteur - Cylindre - Cônes - Sphère - Diamètre # Révision du module ## 4.1 **1.** Draw a net of a square-based pyramid. **Dimensions:** - Base: 6 cm - Height (of each triangular face): 5 cm ## 2.** Which of the following nets does not represent a cube? **a, b, and c** are each diagrams representing nets. ## 4.2 **3.** Match each net with its corresponding object. **a, b, and c** are each diagrams representing nets. **1, 2, and 3** are each diagrams representing objects. ## 4.3 **4.** Determine the area of the net of the rectangular prism. **Dimensions:** - Length: 6 cm - Width: 8 cm - Depth: 6 cm **Calculations:** - Area: (6 cm * 8 cm) + (6 cm * 6 cm) + (8 cm * 6 cm) + (6 cm * 8 cm) + (6 cm * 6 cm) + (8 cm * 6 cm) = __ cm² ## 5.** The surface area of a cube is 384 cm². **a.** What is the edge length of the cube? **Calculations:** - Area of one face: 384 cm² / 6 = __ cm² - Edge length: √ __ cm² = __ cm **b**. What is the volume of the cube? **Calculations** - Volume: __ cm * __ cm * __ cm = __ cm³ ## 6.** a) Draw all possible rectangular prisms with a volume of 8 cm³. Each edge of the prism must have a whole-number length. Record the dimensions of each prism. **Create a table with the following headings:** | Longueur | Largeur | Hauteur | Dessin | |---|---|---|---| | | | | | **b)** Determine the surface area of each prism in the table. ## 4.4 **7.** Determine the total surface area of this prism. **Dimensions:** - Length: 8 m - Width: 6 m