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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. 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. Problem of the Day

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 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 m2, 27 m3

  3. 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 in2

  4. Sunshine State Standards 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.

  5. 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. Additional Example 1: Converting Units of Measure 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. Step 1: Find the area in square inches. A = lw A = lw A = lw A = 13  9 A = 9  4.5 A = 13  4.5 A = 117 in2 A = 40.5 in2 A = 58.5 in2 Multiply each area by 2. A = 2(117 + 40.5 + 58.5) in2 A = 432 in2

  7. Additional Example 1 Continued 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. Step 2: Find the conversion factor for inches to centimeters. 1 inch  2.54 cm

  8. Additional Example 1 Continued 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. Step 3: Convert the area. Square the linear conversion factor. The surface area of the box in square centimeters is 2787.1 cm2.

  9. 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 cm2 1 in2.54 cm 2 75.36 cm2 = 11.68082336 in2 The surface area of the cone is about 11.7 in2.

  10. Additional Example 2: Converting Units of Volume 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? Step 1: Find the volume in cubic centimeters. V = r2h (3.14)(3.25)2(10.7) 354.9 cm3

  11. Additional Example 2 Continued 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? Step 2: Convert the volume. The volume of the can in cubic inches is about 21.7 in3.

  12. Check It Out: Example 2 Find the approximate volume of the cone in cubic feet. 13 V = r2h 13 = (3.14) (1)2 (2) _ = 2.093 m3 1 ft0.3048m _ 2 2.093 m3 = 73.925369 ft3 The volume of the cone is about 73.9 ft3.

  13. Additional Example 3: Application 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 ft2. About how many gallons of a solution does the archaeologist need to cover the lateral area of the pyramid? Step 1: Find the lateral surface area of the pyramid.

  14. Additional Example 3 Continued Step 2: Convert square meters to square feet. 1 m2 10.8 ft2, so 240 m2  2592 ft2. Step 3: Find how many gallons of solution will cover 2592ft2. = 12.96 gal It will take about 13 gallons to cover the lateral area of the pyramid.

  15. Check It Out: Example 3 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.

  16. Check It Out: Example 3 Continued Volume of 1 tile in cubic feet: 12 6 • (3)(2.6)(1) = 23.4 ft3 Volume in cubic yards: 3 1 yd3 ft 23.4 ft3 = 0.87 yd3 3600 lb1 yd3 0.87 yd3• = 3132 lb 1 ton2000 lb 1 tile: 3132 lb = 1.57 tons 40 tiles: 40 • 1.57 tons = 62.8 tons

  17. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  18. Lesson Quiz 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 .  567.74 cm2  671.41 yd3  78.9 s

  19. Lesson Quiz for Student Response Systems 1. Convert. 1 mi3 = ___ yd3 A. 1760 B. 3,097,600 C.5,451,776,000 D.3

  20. Lesson Quiz for Student Response Systems 2. Find the volume. A. 52 in3 B. 52 in2 C.7800 in3 D.7800 in2

  21. Lesson Quiz for Student Response Systems 3. Find the volume. A. 7800 ft3 B. 650 ft3 C.4.5 ft3 D.54.2 ft3

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