Five-Minute Check (over Lesson 11–6) Mathematical Practices Then/Now New Vocabulary Key Concept: Population Density Example 1: Real-World Example: Find Population Densities Example 2: Real-World Example: Apply Population Density Key Concept: Density Example 3: Find the Density of a Solid Example 4: Real-World Example: Compare Densities Lesson Menu

Determine whether the pair of solids is similar, congruent, or neither Determine whether the pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. A. similar; B. similar; C. congruent D. neither 5-Minute Check 1

Two similar cylinders have radii of 12 inches and 16 inches Two similar cylinders have radii of 12 inches and 16 inches. What is the ratio of the surface area of the small cylinder to the surface area of the large cylinder? A. B. C. D. 5-Minute Check 2

Rectangular prism A and rectangular prism B are similar Rectangular prism A and rectangular prism B are similar. Find the volume of rectangular prism B. A. 20 cm3 B. 30 cm3 C. 40 cm3 D. 60 cm3 5-Minute Check 3

Two similar pyramids have surface areas of 45 square feet and 180 square feet. What is the ratio of the height of the large pyramid to the height of the small pyramid? A. 2:1 B. 4:1 C. 8:1 D. 16:1 5-Minute Check 4

Two similar cones have surface areas of 40 square meters and 360 square meters. The volume of the smaller cone is 25 cubic meters. What is the volume of the larger cone? A. 175 m3 B. 225 m3 C. 675 m3 D. 2025 m3 5-Minute Check 5

Mathematical Practices 1 Make sense of problems and persevere in solving them. 4 Model with mathematics. Content Standards G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., person per square mile, BTUs per cubic foot). MP

You found areas of geometric figures and volumes of solids. Solve real-world problems involving density by using area. Solve real-world problems involving density by using volume. Then/Now

population density density New Vocabulary

Key Concept

A. Find the population density of Rhode Island to the nearest tenth. Find Population Densities A. Find the population density of Rhode Island to the nearest tenth. Example 1

Population density ≈ 871.5person/mi2 Find Population Densities Population density ≈ 871.5person/mi2 Answer: 871.5 persons/mi2 Example 1

B. Find the population of Delaware, given that the Find Population Densities B. Find the population of Delaware, given that the population density is 379.7 persons/mi. Example 1

Population ≈ 945,833 Answer: 945,833 Find Population Densities Example 1

Find the area of the park. Apply Population Density A rectangular state park with a length of 2.7 miles and a width of 2.5 miles has a duck population of 2500 ducks. The park rangers want to build a new playground, but can only build the playground if the duck population density is greater than 420 ducks per square mile. Does the population density allow for the playground to be built? 2.7 × 2.5 = 6.75 Find the area of the park. Example 2

Population density ≈ 370.4 ducks/mi2 Can the playground be built? Apply Population Density Population density ≈ 370.4 ducks/mi2 Can the playground be built? The population density is less than 420, so the playground can’t be built. Answer: No; the duck population density is 370.4 ducks/mi2, so the park rangers cannot build the new playground. Example 2

Key Concept

Find the volume of a sphere. Find the Density of a Solid A sphere has a radius of 3 feet. Its mass is 550 grams. Find the density of the sphere to the nearest tenth. Find the volume of a sphere. Density ≈ 4.9 grams/cm3 Answer: 4.9 g/cm3 Example 3

Compare Densities An artist is making a sculpture in the shape of a rectangular prism that is 3 meters long, 180 centimeters wide, and 0.5 meter tall. She wants to be sure that the finished sculpture has a density less than 1.5 grams per cubic centimeter. If she makes the sculpture with clay, it will have a mass of 3780 kilograms. If she makes the sculpture with glass, it will have a mass of 6,480,000 grams. Which material should she use? V = (300)(50)(180) Find the volume of the sculpture. Change the measurements to centimeters. Example 4

Substitute the values for clay into the formula density = Compare Densities Substitute the values for clay into the formula density = Change the kilograms to grams. Substitute the values for glass into the formula density = Clay has a density less than 1.5 grams per cubic centimeters. Answer: clay Example 4