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1 Mr. Whelan Name: Block: Geometry/Trig Unit 10 Area and Volume of Solids Notes Packet
2 Day 1 Notes - Prisms Rectangular Prism: How do we find Total Area? Example 1 6cm Find the area of each face: Front: 8cm Back: Top: Bottom: 10cm Left Side: Right Side: Total: How do you find the Lateral Area? Formula for the Lateral Area of Prism: Formula for the Total Area of Prism: 6m Example 2 6m 20m 9in Example 3 9in 9in
3 Volume: Units: Formula for Volume of Prism: Revisit Example 1: Dimensions: 6cm, 8cm, 10cm Volume: Revisit Example 2: Dimensions: 6m, 6m, 20m Volume: Revisit Example 3: Dimensions: 9in, 9in, 9in Volume: Example 4: Find the Lateral Area, Total Area, and Volume of the rectangular prism. 7in 5in 13in Volume:
4 V = Bh Volume (V) = Area of the Base x height of the prism LA = ph TA = LA + 2B Lateral Area (LA) = Perimeter of Base x height Total Area (TA) = Lateral Area + 2(Area of the Base) p = Perimeter of Base h = height of Prism B = Area of Base Example 1: Find the Lateral Area, Total Area and Volume of the Triangular Right Prism. 12m This is the base of the figure. 8m 7m 12m 12m 8m 4m 7m Area of the Base: Perimeter of the Base: Height: Volume: Example 2: Find the Lateral Area, Total Area and Volume of the Triangular Right Prism. Volume: 14m 10m 6m 10m 16m
5 Example 3: Find the Lateral Area, Total Area and Volume of the Trapezoidal Right Prism. 30m Volume: 40m 10m 14m 8m 18m Example 4: Find the Lateral Area, Total Area and Volume of the Hexagonal Right Prism. 6cm Volume: 12cm 6cm Base is a Regular Hexagon
6 Day 1 Practice Find the Volume, Lateral Area, and Total Area of each figure. Figure Volume Area 1. 42m 24m 36m 12m 18m m 42m 24m 20m 18m 28m m 75m 70m
7 Day 2 Notes - Pyramids Regular Pyramid - We will be looking at square pyramids. Lateral Area - Total Area - Volume - Therefore, we need to find the following four pieces of information for each problem: Example 1 8in = h 12in = e 1. Area of the base A = e 2 2. Perimeter of the base P = 4e 3. Height h 4. Slant height - l Base Edge - Height Slant Height 10in = l Area of the base Perimeter of the base - Lateral Area - Total Area - Volume -
8 Example 2 24in 26in Base Edge - Height Slant Height Area of the base Perimeter of the base - Lateral Area - Total Area - Volume - Example 3-16ft 15ft Base Edge - Height Slant Height Area of the base Perimeter of the base - Lateral Area - Total Area - Volume -
9 Day 2 Notes Spheres Sphere - Volume - Total Area - Example 1 Find the Total Area and Volume of the Sphere Radius - 6in Volume - Total Area -
10 Day 2 Practice Spheres Example 2 Find the Total Area and Volume of the Sphere 15mm Radius - Volume - Total Area - Example 3 Find the Total Area and Volume of the Sphere C = 20pin Radius - Volume - Total Area -
11 Mixed Review 1. Figure Volume Area 4m Name: 2. 15m 8m Name: cm 2cm Name:
12 Mixed Review Figure Volume Area 1. 6m 7m 10m Name: ft Name: 3. 13m 12m Name:
13 Day 3 Notes Cylinders A cylinder is like the right prisms except that the bases of a cylinder are. The volume and total area can be calculated in a very similar manner. In a cylinder, the formula for Volume is exactly the same. Multiply the Area of the Base (B) by the height (h). In this case the base is a circle. Recall that the area of a circle is calculated by using A =. The Lateral Area and Total Area is calculated in a similar manner. However we must replace perimeter of base with, use Formulas: LA = TA = V = Example 1 Find the Total Area and Volume of the given cylinder. Radius Area of Base Height Volume Lateral Area 10in Total Area - 4in
14 Example 2 14m Radius Area of Base Height 7m Volume Lateral Area - Total Area Example 3 Radius Area of Base Height 75cm Volume 100cm Lateral Area - Total Area -
15 Day 3 Notes Cones Cone - Volume - Lateral Area - Total Area - Therefore, now we need to find the four key pieces of information first: 1. Area of the base 2. Height - 3. Slant height - Example 1 Find the Volume and Total Area Radius - Area of the base 10m Height - Slant height 6m Lateral Area - Total Area - Volume -
16 Example 2 Find the Volume and Total Area Radius - Area of the base Height - Slant height 12m Lateral Area - Total Area - Volume - 9m Example 3 Find the Volume and Total Area Radius - Area of the base Height - Slant height 26cm 24cm Lateral Area - Total Area - Volume -
17 Cylinders Practice 1. Figure Volume Area 47ft 13ft 2. 2ft 24ft 3. 5in 1in page 5
18 Cones Practice 1. Figure Volume Area 17in 2. 8in 24ft 20ft 3. 12cm 5cm page 6
19 Day 4 Notes Similar Solids Theorem 12-1 If the scale factor of two similar solids is a:b, then 1. The ratio of their perimeters is a:b. 2. The ratio of their base areas, lateral areas, and total areas is a 2 :b The ratio of their volumes is a 3 :b 3 Given the solids, determine the ratio of their totals areas and their volumes. Example 1: 6 Cubes 10 Scale Factor: Ratio of Total Areas: All cubes are. Example 2: Ratio of Volumes: Scale Factor: 3 Similar Cylinders 2 Ratio of Total Areas: Ratio of Volumes: Example 3: All spheres are. 8 2 Scale Factor: Ratio of Total Areas: Spheres Ratio of Volumes: 1.) 2.) 3.)
20 Day 4 Practice 1. Two similar polygons have a scale factor of 3:5. What is the ratio of the perimeters? What is the ratio of the areas? 2. Two circles have radius lengths 4 and 12. What is the scale factor? What is the ratio of circumferences? What is the ratio of areas? 3. The ratio of areas of two squares is 9:16. What is the ratio of their perimeters? What is the ratio of their side lengths? 4. The ratio of areas of two similar polygons is 9:625. The perimeter of the smaller polygon is 12. What is the perimeter of the larger polygon? 5. The ratio of perimeters of two similar polygons is 4:15. The area of the larger polygon is 64. What is the area of the smaller polygon? 6. Two similar solids have a scale factor of 3:7. What is the ratio of their lateral areas? What is the ratio of their total areas? What is the ratio of their volumes? 7. Two spheres have diameters with lengths 10 and 20. What is the ratio of their radii? What is the ratio of their circumferences? What is the ratio of their total areas? What is the ratio of their volumes? 8. The ratio of volumes of two cubes is 27:2744. What is the scale factor? What is the ratio of lateral areas? What is the ratio of total areas? What is the perimeter of the base of the larger cube? 9. The ratio of lateral areas of two similar solids is 25:36. What is the ratio of their volumes? 10. The ratio of total areas of two similar solids is 64:81. If the volume of the smaller solid is 1024, what is the volume of the larger solid? 11. The ratio of volumes of two similar solids is 1:729. The lateral area of the larger solid is 324, what is the lateral area of the smaller solid?
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