UNIT 4: LENGTH, AREA, AND VOLUME WEEK 16: Student Packet

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Name Period Date UNIT 4: LENGTH, AREA, AND VOLUME WEEK 16: Student Packet 16.1 Circles: Area Establish the area formula for a circle. Apply the area formula for a circle to realistic problems.

1 Name Period Date UNIT 4: LENGTH, AREA, AND VOLUME WEEK 16: Student Packet 16.1 Circles: Area Establish the area formula for a circle. Apply the area formula for a circle to realistic problems. Demonstrate understanding of the area of a circle with symbols, tables, graphs, and words Cylinders: Volume and Surface Area Derive the formulas for surface area and volume of cylinders. Compute the surface area and volume of cylinders Review 1 Review mathematical concepts from the first semester. Demonstrate competency in solving equations (highlighted review) Week 16 SP

2 FOCUS ON VOCABULARY 16 Match the words to the clues and draw a picture next to the word. Words Clues 1. volume a. The total area of the surface of a solid. It is measured in square units. 2. base b. A face of a three-dimensional figure that is perpendicular to its height. 3. radius c. The measure of the interior of a solid, measured in cubic units. 4. surface area d. A solid figure with two circular, congruent bases that are parallel to each other. 5. area of a circle e. A line segment from the center of a circle to any point on the circle. 6. cylinder f. This is the product of pi and the square of the radius. Week 16 SP0

3 16.1 Circle: Area CIRCLE: AREA Ready (Summary) We will use formulas for the area of a rectangle and the circumference of a circle to help us find a formula for the area of a circle. Set (Goals) Establish the area formula for a circle. Apply the area formula for a circle to realistic problems. Demonstrate understanding of the area of a circle with symbols, tables, graphs, and words. Go (Warmup) The diameter of a dinner plate is 12 cm. Find its radius and circumference. Picture: Numbers/Symbols: Words: Week 16 SP1

4 16.1 Circle: Area THE AREA OF A CIRCLE 1. What is the formula for the circumference of a circle in terms of its radius r? 2. Your teacher will give you a piece of paper with a circle on it. Cut out the circle and fold it in half. Fold it in half a second time. Fold it in half a third time. 3. Unfold your circle and cut along the folds to make 8 wedges. (You may want to try more than 8 wedges, like 16, but don t do less.) 4. Arrange the wedges in a row. Alternate the tips up and down to form a shape that resembles a rectangle or parallelogram. Tape, glue stick, or sketch the shape here. Use your knowledge of the area of a rectangle and circumference of a circle to find the area of this shape. (Remember, it began as a circle and is becoming closer to resembling a rectangle. The more wedges you make, the closer it gets to becoming a rectangle.) 5. The width of the rectangle is the of the circle. 6. The length of the rectangle is of the circle. 7. Write an equation for the approximate area of the rectangle. 8. Substitute the expression for the circumference of the circle from #1 above into your formula and simplify. 9. What is the formula for the area of a circle, in terms of the radius? Week 16 SP2

5 16.1 Circle: Area AREA OF A CIRCLE: THE FOURFOLD WAY 1. Symbols: What is a formula for finding the area of a circle? 2. Table: Use the formula to calculate the area of a circle with the given radius. Length of radius (r) (show work) Area of circle (A) 0 1 Area (A) radius (r) 3. Graph: Make a graph that compares area (A) and radius (r). 4. Words: Explain how you would find the area of a circle if you knew the diameter. Week 16 SP3

6 16.1 Circle: Area USE YOUR CIRCLE KNOWLEDGE 2 1. The dish problem: Find the area of a plate whose diameter is 12 inches. Picture: Numbers/Symbols: Words: 2. The water sprinkler problem: A revolving water sprinkler sprays water in a circular fashion to a distance of 20 feet in all directions. What area of grass can it cover? Picture: Numbers/Symbols: Words: Week 16 SP4

7 16.1 Circle: Area USE YOUR CIRCLE KNOWLEDGE 2 (continued) 3. The pizza problem: Pizza House sells 2 different pizza sizes: A 16-inch-diameter pizza and a 12-inch-diameter pizza. How much more pizza do you get by ordering the 16 in. diameter pizza than the smaller one? Picture: Numbers/Symbols: Words: 4. The school track problem: A field at a local school is surrounded by a track. Each straightaway is 425 feet. The distance across the field (top to bottom in the diagram) is 150 feet. Find the area of the field. Picture: Numbers/Symbols: straightaway Words: Week 16 SP5

8 16.2 Cylinders: Volume and Surface Area CYLINDERS: VOLUME AND SURFACE AREA Ready (Summary) We will make sense of the formulas for the surface area and volume of cylinders and apply them to solve problems. Set (Goals) Derive the formulas for surface area and volume of cylinders. Compute the surface area and volume of cylinders. Go (Warmup) 1. The formula for finding the circumference of a circle is: 2. The formula for finding the area of a circle is: A circle has circumference C = inches. 3. Find the radius of the circle. 4. Find the area of the circle. A rectangular prism measures 2 ft. 5 ft. 6 ft. 5. Find the surface area of the prism. 6. Find the volume of the prism. Week 16 SP6

9 16.2 Cylinders: Volume and Surface Area A PAPER CYLINDER Roll a letter-size piece of paper parallel to the 8 1 -inch sides to make a cylinder. Tape 2 the two 8 1 -inch edges together. Imagine your cylinder has two circular bases, or cut 2 out two circular bases and tape them to the top and bottom of the cylinder. 1. Sketch a net of the cylinder and label its dimensions. 2. Sketch the cylinder and label its dimensions. 3. Find the surface area rounded to the nearest hundredth. Formula: SA = Substitute: 4. Find the volume rounded to the nearest hundredth. Formula: V = Substitute: Answer: sq. in. Answer: cu. in. Week 16 SP7

10 16.2 Cylinders: Volume and Surface Area ANOTHER PAPER CYLINDER Roll a letter-size piece of paper parallel to the 11-inch sides to make a cylinder. Tape the two 11-inch edges together. Imagine your cylinder has two circular bases, or cut out two circular bases and attach them to the top and bottom of the cylinder. 1. Sketch a net of the cylinder and label its dimensions. 2. Sketch the cylinder and label its dimensions. 3. Find the surface area rounded to the nearest hundredth. Formula: SA = Substitute: 4. Find the volume rounded to the nearest hundredth. Formula: V = Substitute: Answer: sq. in. Answer: cu. in. Week 16 SP8

11 16.2 Cylinders: Volume and Surface Area CIRCULAR BASES FOR PAPER CYLINDERS Trace two sets of the circles below and cut them out to use as bases for your cylinders. Week 16 SP9

12 16.3 Review 1 SKILL BUILDER 1 Show your work on a separate sheet of paper and choose the best answer. 1. Which properties of arithmetic are illustrated in the equation ( ) + 78 = 15 + (32+78)? A. commutative property of addition B. associative property of addition C. distributive property D. all of the above 2. What does the 8 represent in 45,389,011? E. 8,000 F. 80,000 G. 800,000 H. 10, Which properties of arithmetic are illustrated in the equation = 24 18? A. commutative property of multiplication B. associative property of multiplication C. distributive property D. all of the above 4. Compute E. 205 F. 105 G. 195 H Compute A. 3,408 B. 3,308 C. 852 D (3 5) E. 75 F. 135 G. 3 H What are the prime factors of 24? A B C D Evaluate the expression 3x + 7 for x = 6. E. 25 F. 60 G. 39 H. 24 Week 16 SP10

13 16.3 Review 1 SKILL BUILDER 2A Compute Week 16 SP11

14 16.3 Review 1 SKILL BUILDER 2B Solve = 3( x 2) 11. 2( x 2) = 4x x + 2 = 4(2 + x) 13. Extend the geometric pattern, write a rule and make a graph. A Geometric Pattern Table Step 1 Step 2 Step # (Input) x (Output) y 1 9 Graph Step Step Step 5 x y = 14. Describe the geometric and numerical patterns in words: Week 16 SP12

15 16.3 Review 1 SKILL BUILDER 3A Compute Solve for x. 4. -( x+ 3) = 4x x 4 = = 3( x 4) 7. Complete the table, graph the values, and write an equation for the line. There are 4 quarts in a gallon. gallons (x) x quarts (y) y = Week 16 SP13

16 16.3 Review 1 SKILL BUILDER 3B Show your work on a separate sheet of paper and choose the best answer. 8. What is the value of the expression (13 + 4) (7 2) + (31 17)? A. 45 B. 40 C. 17 D The letters m and n stand for numbers. If m 100 = n 100, which of the following statements is true? E. m = n F. m > n G. m = n H. m > n What number goes in the box to make the number sentence true? (7 3) 5 = 4 A. 5 B. 3 C. 7 D What is the value of y if y 2 = 10? E. 12 F. 10 G. 8 H What value of k makes the equation k 3 = 36 true? A B. 12 C. 33 D Which equation could have been used to create this function table? x y E. y = 2 x F. y = 2x G. y = x 4 H. y = x Which of the following numbers has the greatest value? A. 0.3 B C. -2 D. 4 5 Week 16 SP14

17 16.3 Review 1 TEST PREPARATION 16 Show your work on a separate sheet of paper and choose the best answer. 1. What is the surface area of a cylinder that has a base with a diameter of 18 ft. and a height of 13 ft? A. 234 ft. 2 B ft. 2 C. 1, ft. 2 D. 3, ft The largest possible circle is to be cut from a 10-foot square board. What will be the approximate area, in square feet, of the remaining board (shaded region)? E. 30 F. 50 G. 20 H Solve 5 2x = 7 for x. A. x = 1 B. x = -1 C. x = 6 D. x = Compute E F G. 2 5 H Compute A B C. 6.5 D. 65 Week 16 SP15

18 16.3 Review 1 This page is left intentionally blank for notes. Week 16 SP16

19 16.3 Review 1 KNOWLEDGE CHECK 16 Show your work on a separate sheet of paper and write your answers on this page Circles: Area 1. Find the area of a circular tabletop with a radius of 2.5 feet. 2. Find the area of the circle rounded to the nearest tenth of a square unit. 2.2 mm 16.2 Cylinders: Volume and Surface Area A cylinder has a base with a diameter of 5 ft. and a height of 16 ft. 3. Sketch a net for the cylinder and label the dimensions. 4. Find the surface area of the cylinder. Highlighted Review: Solving Equations Solve for x x = ( x 1) = = 2( x + 6) Week 16 SP17

20 16.3 Review 1 Home-School Connection 16 Here are some questions from this week s lessons to review with your young mathematician. 1. Find the area of the circle rounded to the nearest tenth. 5.4 cm 2. A cylinder has a base with a diameter of 6.2 mm and a height of 4.5 mm. Find its surface area. 3. A cylinder has a base with a radius of 5 mm and a height of 4 mm. Find the volume. Parent (or Guardian) signature Selected California Mathematics Content Standards MG MG Know common estimates of π (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Week 16 SP18

Sample: Do Not Reproduce GEO1 STUDENT PAGES. GEOMETRY AND MEASUREMENT Student Pages for Packet 1: Length and Area.

Sample: Do Not Reproduce GEO1 STUDENT PAGES. GEOMETRY AND MEASUREMENT Student Pages for Packet 1: Length and Area. Name Period Date GEOMETRY AND MEASUREMENT Student Pages for Packet 1: GEO1.1 Congruence Plot simple figures on coordinate graphs, and determine their lengths and areas. Make conjectures about perimeters