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

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

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

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.

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( ) in 2 A = 432 in 2

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

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 cm 2.

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) (3)(5) = = cm cm 2 = in 2 1 in 2.54 cm 2 The surface area of the cone is about 11.7 in 2.

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)  cm 3

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.

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 = (3.14) (1) 2 (2) 1313 = m 3 _ m 3 = ft 3 _ 1 ft m 2

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.

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. = gal It will take about 13 gallons to cover the lateral area of the pyramid.

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

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 Volume in cubic yards: 23.4 ft 3 = 0.87 yd 3 1 yd 3 ft yd 3 = 3132 lb 3600 lb 1 yd 3 1 tile: 3132 lb = 1.57 tons 1 ton 2000 lb 40 tiles: tons = 62.8 tons

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

Measurement in Three-Dimensional Figures 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  yd 3  cm 2  78.9 s

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

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

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