1. Measurement in Three-Dimensional Figures 9-10 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Measurement in Three-Dimensional Figures 9-10 Warm Up Fill in the blanks. 1. 1 yd = ___ in. 2. 1 mi  ___ ft 3. 1 mi  ___ km 4. Find the surface are and volume of a cube with a side length of 3 meters. 36 3.28 1.6 54 m 2, 27 m 3

3. Measurement in Three-Dimensional Figures 9-10 Problem of the Day Chris cuts 1 in. by 1 in. squares from the corners of an 8.5 in. by 11 in. paper and fold the sides up to form an open box. What is the volume of a box? 58.5 in 2

4. Measurement in Three-Dimensional Figures 9-10 MA.8.G.5.1 Compare, contrast, and convert units of measure between different measurement systems (U.S. customary or metric (SI)) and dimensions including…area, volume, and derived units to solve problems. Sunshine State Standards

5. Measurement in Three-Dimensional Figures 9-10 You can convert units of area and volume. For example, you can draw a diagram to help you convert square feet to square inches. You can convert units of area by squaring the linear conversion factor.

6. Measurement in Three-Dimensional Figures 9-10 A shoebox has a length of 13 inches, a width of 9 inches, and a height of 4 1/2 inches. Find the surface area of the box in square centimeters. Additional Example 1: Converting Units of Measure Multiply each area by 2. Step 1: Find the area in square inches. A = lw A = 13  9 A = 117 in 2 A = lw A = 9  4.5 A = 40.5 in 2 A = lw A = 13  4.5 A = 58.5 in 2 A = 2(117 + 40.5 + 58.5) in 2 A = 432 in 2

7. Measurement in Three-Dimensional Figures 9-10 Step 2: Find the conversion factor for inches to centimeters. 1 inch  2.54 cm A shoebox has a length of 13 inches, a width of 9 inches, and a height of 4 1/2 inches. Find the surface area of the box in square centimeters. Additional Example 1 Continued

8. Measurement in Three-Dimensional Figures 9-10 Square the linear conversion factor. A shoebox has a length of 13 inches, a width of 9 inches, and a height of 4 1/2 inches. Find the surface area of the box in square centimeters. Additional Example 1 Continued Step 3: Convert the area. The surface area of the box in square centimeters is 2787.1 cm 2.

9. Measurement in Three-Dimensional Figures 9-10 Check It Out: Example 1 A cone has a radius of 3 centimeters, a height of 4 centimeters, and a slant height of 5 centimeters. What is the surface area of the cone in square inches to the nearest tenth? Use 3.14 for π. S = 3.14(3) 2 + 3.14(3)(5) = 28.26 + 47.1 = 75.36 cm 2 75.36 cm 2 = 11.68082336 in 2 1 in 2.54 cm 2 The surface area of the cone is about 11.7 in 2.

10. Measurement in Three-Dimensional Figures 9-10 A standard beverage can is a cylinder with a radius of 3.25 cm and a height of 10.7 cm. What is the volume of the can in cubic inches to the nearest tenth? Additional Example 2: Converting Units of Volume Step 1: Find the volume in cubic centimeters. V = r 2 h  (3.14)(3.25) 2 (10.7)  354.9 cm 3

11. Measurement in Three-Dimensional Figures 9-10 A standard beverage can is a cylinder with a radius of 3.25 cm and a height of 10.7 cm. What is the volume of the can in cubic inches to the nearest tenth? Additional Example 2 Continued Step 2: Convert the volume. The volume of the can in cubic inches is about 21.7 in 3.

12. Measurement in Three-Dimensional Figures 9-10 Find the approximate volume of the cone in cubic feet. Check It Out: Example 2 V = r 2 h The volume of the cone is about 73.9 ft 3. 1313 = (3.14) (1) 2 (2) 1313 = 2.093 m 3 _ 2.093 m 3 = 73.925369 ft 3 _ 1 ft 0.3048m 2

13. Measurement in Three-Dimensional Figures 9-10 An archaeologist wants to apply a liquid solution to the lateral area of a square pyramid as a protectant. Each side of the square base measures 12 meters and the slant height is 10 meters. One gallon of solution covers 200 ft 2. About how many gallons of a solution does the archaeologist need to cover the lateral area of the pyramid? Additional Example 3: Application Step 1: Find the lateral surface area of the pyramid.

14. Measurement in Three-Dimensional Figures 9-10 Additional Example 3 Continued Step 2: Convert square meters to square feet. 1 m 2  10.8 ft 2, so 240 m 2  2592 ft 2. Step 3: Find how many gallons of solution will cover 2592 ft 2. = 12.96 gal It will take about 13 gallons to cover the lateral area of the pyramid.

15. Measurement in Three-Dimensional Figures 9-10 The concrete tile shown is a hexagonal prism. A cubic yard of concrete weighs about 3600 pounds. What is the weight of 40 tiles in tons. Check It Out: Example 3

16. Measurement in Three-Dimensional Figures 9-10 Check It Out: Example 3 Continued Volume of 1 tile in cubic feet: 6 (3)(2.6)(1) = 23.4 ft 3 1212 Volume in cubic yards: 23.4 ft 3 = 0.87 yd 3 1 yd 3 ft 3 0.87 yd 3 = 3132 lb 3600 lb 1 yd 3 1 tile: 3132 lb = 1.57 tons 1 ton 2000 lb 40 tiles: 40 1.57 tons = 62.8 tons

17. Measurement in Three-Dimensional Figures 9-10 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

18. Measurement in Three-Dimensional Figures 9-10 1. A triangle has a base of 8 inches and a height of 22 inches. Find the area of the triangle in square centimeters. 2. Find the volume of the pyramid in cubic yards. 3. A child is coloring a circle with a radius of 9 centimeters at a rate of 0.5 square inch per second. How long will it take the child to color the circle? Use 3.14 for . Lesson Quiz  671.41 yd 3  567.74 cm 2  78.9 s

19. Measurement in Three-Dimensional Figures 9-10 1. Convert. 1 mi 3 = ___ yd 3 A. 1760 B. 3,097,600 C. 5,451,776,000 D. 3 Lesson Quiz for Student Response Systems

20. Measurement in Three-Dimensional Figures 9-10 2. Find the volume. A. 52 in 3 B. 52 in 2 C. 7800 in 3 D. 7800 in 2 Lesson Quiz for Student Response Systems

21. Measurement in Three-Dimensional Figures 9-10 3. Find the volume. A. 7800 ft 3 B. 650 ft 3 C. 4.5 ft 3 D. 54.2 ft 3 Lesson Quiz for Student Response Systems