Lesson 1 - Area Review Shape Words Formula

Transcription

1 Lesson 1 - Area Review Shape Words Formula Rectangle The area A of a rectangle is the product of the length and the width w. A = w Parallelogram The area A of a parallelogram is the product of any base b and its height h. Find the area of each figure. Show your work. A = bh

2 Lesson 2 More Area Review Shape Words Formula Triangle The area A of a triangle is half the product of any base b and its height h. A = bh Trapezoid The area A of a trapezoid is half the product of the height h and the sum of the bases, b1 and b2. Find the area of each figure. Show your work. A = h (b1 + b2)

3 Lesson 3- Circumference center The diameter, d, is the distance across a circle through its center. The circumference, C, is the distance around a circle The radius, r, is the distance from the center to any point on a circle. The diameter of a circle is twice its radius. d = 2r The radius is half the diameter. r = The circumference of a circle is equal to π times its diameter or π times twice its radius. Examples The radius of a circle is 7 meters. Find the diameter. Write the formula. d = 2r Replace r with 7 d = 2 7 Multiply d = 14 The diameter is 14 meters. 7 m C = πd C = 2πr Find the circumference of a circle with a radius that is 13 inches. Use 3.14 for π. Round to the nearest tenth. Write the formula. C = 2πr Replace r with 13 and π with C Multiply. C Rounded to the nearest tenth, the circumference is about 81.6 inches. Find the circumference of each circle. Use 3.14 for π. Round to the nearest tenth if necessary. Show your work m 8 in. 21 ft

4 Lesson 4 - Area of Circles The area A of a circle equals the product of pi (π) and the square of its radius r. A = πr 2 The formula for the area of a semicircle, or half a circle, is A = πr 2. Examples Find the area of the circle. Use 3.14 for π. 5 cm Find the area of a semicircle that has a diameter of 9.4 millimeters. Use 3.14 for π. Round to the nearest tenth. A = πr 2 Area of semicircle Area of circle A = πr 2 Replace π with 3.14 and r with 5. A = 5 5 = 25 A A 78.5 The area of the circle is approximately 78.5 square centimeters. A Replace π with 3.14 and A 34.7 r with or 4.7. Multiply. The area of the semicircle is approximately 34.7 square millimeters. Find the area of each circle. Round to the nearest tenth. Use 3.14 for π. Show your work in 25 mm 12 ft Find the area of each semicircle. Round to the nearest tenth. Use 3.14 π. Show your work m 3 ft GARDENING Vidur needs to buy mulch for the garden with the dimensions shown in the figure. For how much area does Vidur need to buy mulch? 5.5 yd

5 Extended Constructed Response Question Show your work & explain your answer. John is scuba diving in the ocean. He begins at a depth of -232 feet. He swims down 87 feet to check out a shipwreck, and then back up 101 feet when he sees a sting ray. 1. What is his current depth? 2. Draw a number line and record the three depths he hits. For example, you would place a dot at -232 and label this starting depth. You must place his depth after he swims down, and after he swims back up. (there will be three dots on your number line). 3. If 1 ft = 12 in, how many inches under water was John when he started? Explain your answer.

6 Lesson 5- Area of Composite Figures To find the area of a composite figure, decompose the figure into shapes whose areas you know how to find. Then find the sum of these areas. Example Find the area of the composite figure. The figure can be separated into a semicircle and trapezoid. Then, add the areas together. The area of the figure is about or 237 square inches. Area of semicircle Area of trapezoid 14 in. 10 in. 18 in. 14 in. A = πr 2 A = h(b1 + b2 ) 10 in. A = π (7) 2 A 77.0 in 2 14 in. A = 10 ( ) A = 160 in 2 18 in. Find the area of each figure. Round to the nearest tenth if necessary. Use 3.14 for π. Show your work mm 5 mm 6 mm 6 ft 9 ft 7 mi 14 mi 5 mi 5 mi 9 ft 4. SWIMMING POOLS The Cruz family is buying a custom-made cover for their swimming pool, shown below. The cover costs $2.95 per square foot. How much will the cover cost? Round to the nearest cent. 15 ft 25 ft

7 Lesson 6 - Volume of Prisms The volume of a three-dimensional shape is the measure of space occupied by it. It is measured in cubic units such of the shape at the right can be shown using cubes. The bottom layer, or base, has 4 3 or 12 cubes. There are two layers. It takes 12 2 or 24 cubes to fill the box. So, the volume of the box is 24 cubic meters. A rectangular prism is a three-dimensional shape that has two parallel and congruent sides, or bases, that are rectangles. To find the volume of a rectangular prism, multiply the area of the base times the height, or find the product of the length, the width w, and the height h. V = Bh or V = wh Example Find the volume of the rectangular prism V = wh Volume of a rectangular prism V = Replace with 5, w with 6, and h with 8. V = 240 Multiply. The volume is 240 cubic inches. Find the volume of each prism. Round to the nearest tenth. Show your work STICKY NOTES A triangular box of sticky notes is shown. Find the volume of the box.

8 ANSWERS: Homework Mid-Unit Test Review Calculate the correct answer to each problem. When finished, check your answers. Use 3.14 for π. Round to the nearest tenth. Show your work. 1. What is the circumference of the circle? A yd C yd B yd D yd 28.1 yd 2. What is the area of the circle? A. 1,017.4 mm 2 C mm 2 B mm 2 D mm 2 9 mm 3. A rectangular trunk has a volume of 26,880 cubic inches. The trunk is 4 feet long by 28 inches wide. What is the trunk's height? A. 20 in. C. 240 in. B. 60 in. D. 2,880 in. 4. What is volume of the right triangular prism? A. 93.3m 3 C. 280 m 3 B m 3 D. 560 m 3 4 m 10 m 14 m 5. What is the area of the figure? 1C, 2B, 3C, 4C, cm 2 18 cm 36 cm

9 Extended Constructed Response Question Show your work & explain your answer. Bart, Lisa and Maggie Simpson order pizza for dinner to share. Bart eats of a pizza, Lisa eats of a pizza and Maggie eats of a pizza. 1. Put the Simpsons in order from who eats the most pizza to who eats the least amount. 2. Create two equivalent fractions for the pizza Maggie ate. Draw a picture to show they are equivalent. 3. Is there any pizza left for Homer? If so, how much?

10 Lesson 7 - Comparing Volume Lab Cylinder Volume = πr 2 h Surface Area = 2πrh + 2πr 2 h r Cone Volume = πr 2 h Find the volume of each shape. Round to the nearest tenth. Use 3.14 for π. Show your work in 3 in 3. The track-and-field club is planning a frozen yogurt sale to raise money. They need to buy containers to hold the yogurt. They must choose between the cup and the cone below. Each container costs the same. The club plans to charge customers $1.25 for a serving of yogurt. Which container should the club buy? Why?

11 Lesson 8 - Volume of Pyramids A pyramid is a three-dimensional shape with one base and triangular lateral faces. The volume V of a pyramid is one third the area of the base B times the height h. V = Bh Examples Find the volume of the pyramid. Round to the nearest tenth. V = Bh Volume of a pyramid 11 m V = ( w)h The base is a rectangle, so B = w. 4.3 m 3.2 m V = ( ) 11 = 4.3, w = 3.2, h = 11 V 50.5 Simplify. The volume is about 50.5 cubic meters. Find the volume of each shape. Round to the nearest tenth. Show your work cm 10 in. 7 in. 10 in. 8 cm 7 cm 13 in. 16 in 2.3 in. 4. GATE POST The top of a gate post is in the shape of a square pyramid. The height of the pyramid is 5 inches and each side of the base is 7.4 inches. Find the volume of wood needed. to make the top of the gate post

12 Extended Constructed Response Question Show your work & explain your answer. Use your reference sheet. The can of soup below has a radius of 4 cm and a height of 12 cm 1. What is the volume of the soup can? 2. Jeremy eats 65% of the soup for lunch. How much soup did he eat? 3. If Jeremy wants to pour the soup in the can into a Rubbermaid container (a square prism) that has a side length of 6 cm and a height of 10 cm, how much space will be left in the container??

13 Lesson 9 - Nets of 3-D Figures Lab A net is a 2-D pattern for a 3-D shape. Can the pattern be folded along the lines to form a closed rectangular box? Explain for each pattern. 1. YES NO 2. YES NO 3. YES NO 4. YES NO 5. YES NO 6. YES NO

14 Lesson 10 Surface Area of Prisms The sum of the areas of all the surfaces, or faces, of a three-dimensional shape is the surface area. The surface area S.A. of a rectangular prism with length, width w, and height h is the sum of the areas of its faces. S.A. = 2 w + 2 h + 2wh Examples Find the surface area of the rectangular prism. Faces Area 3 cm 4 m 3 cm 3 m 7 cm 2 m 2 m 4.9 ft top and bottom 2 (4 3) = 24 front and back 2 (4 2) = 16 two sides 2 (2 3) = 12 sum of the areas = 52 Alternatively, replace with 4, w with 3, and h with 2 in the formula for surface area. S. A. = 2 w + 2 h + 2wh = 2 (4 3) + 2 (4 2) + 2 (3 2) = = 52 So, the surface area of the rectangular prism is 52 square meters. 4 m back 4 m 2 m side bottom side 2 m 3 m front top 3 m Find the surface area of each prism. Show your work ft 0.7 ft 8 mm 15 mm 17 mm 9 mm 4. CONTAINERS A company needs to package hazardous chemicals in special plastic rectangular prism containers that hold 80 cubic feet. Find the whole number dimensions of the container that would use the least amount of plastic.

15 Lesson 11 Relating Surface Area and Volume Lab Surface Area of a Rectangular Prism = 2 w + 2 h + 2wh Volume of a Rectangular Prism = wh To find the surface area of a triangular prism, it is more efficient to find the area of each face and calculate the sum of all the faces rather than use a formula Each of these boxes holds 36 ping-pong balls. Volume of a Prism = Bh Box D Box A Box B Box C 1. Without figuring, which box has the least surface area? Explain. Find the surface area of each box. Show your work Draw a sketch of a triangular prism with a volume of 120 cubic units and a surface area of 184 square units. Label the dimensions. HINT: The triangle is an isosceles triangle with two sides with a length of 5 units.

16 ANSWERS: 1B, 2B, 3C, 4C, 5-14 in Homework Mid-Unit Test Review Calculate the correct answer to each problem. When finished, check your answers. Show your work. Round to the nearest tenth, if necessary. 1. What is the volume of the pyramid? A. 32 in 3 C. 72 in 3 B. 48 in 3 D. 144 in 3 6 in. 4 in. 6 in. 2. What is the volume of the pyramid? A. 2,352 m 3 C. 1,176 m 3 B. 392 m 3 D m 3 7 m 24 m 14 m 25 m 3. What is the surface area of the figure? A. 185 m 2 C. 370 m 2 B. 231 m 2 D. 462 m 2 6 m 4. What is volume of the right triangular prism? A. 134 ft 2 C. 288 ft 2 B. 144 ft 2 D. 336 ft 2 11 m 12 ft 6 ft 8 ft 10 ft 7 m 5. A drawer is shaped like a rectangular prism. It has a length of 17 inches and a height of 6 inches. The volume is 1,428 cubic inches. Find the width of the drawer. Remember: your test will include all the lessons from the start of the unit. Go back over all previous materials.

17 Extended Constructed Response Question Show your work & explain your answer. A company will make a cereal box with whole number dimensions and a volume of 100 cubic centimeters. 1. Make a list of all the possible box dimensions. 2. If cardboard costs $0.05 per 100 square centimeters, what is the least cost to make 100 boxes? Explain.

18 Lesson 12 Surface Area of Pyramids The total surface area S.A. of a regular pyramid is the lateral area L.A. plus the area of the base. S.A. = B + L.A. or S.A. = B + P Examples Find the total surface area of the pyramid. 6 in. Find the total surface area of the pyramid. 5 m Perimeter of base P Slant height Area of base B Surface area of a pyramid S.A. = B + P 7 in. 7 in. S.A. = 49 + (28 6) P = 4(7)= 28, = 6, B = 7 7= 49 S.A. = 133 Simplify. The surface area of the pyramid is 133 square inches. 6 m 6 m 6 m S.A. = (18 5) P = 3(6)= 18, = 5, B = 15.6 S.A. = 60.6 area of base 15.6 m 2 Simplify. The surface area of the pyramid is 60.6 square meters. Find the total surface area of each pyramid. Round to the nearest tenth. Show your work ft 3 ft 2 ft 4 cm 4 cm 4 cm 7 cm TENT The Summers children are camping out in the tent shown. Find the lateral area of the tent. 9 ft. area of base 6.9 cm 2 12 ft. 12 ft.

19 Lesson 13-Volume of Composite Figures Find the volume of each shape, then add together. Example The figure is made up of a rectangular prisms. V = lwh + lwh V = V = The volume of the composite figure is 2.5 cubic meters. Find the volume of the composite figure. Show your work ft 10 ft 4 in 20 ft 10 ft 4 in 8 in 10 in 4. Draw an example of a composite figure that has a volume between 250 and 300 cubic units.

20 Lesson 14- Surface Area of Composite Figures The circle, is A = πr 2. Example To find the surface area, find the area of exposed surfaces. The lateral area of the prism is = 120 m 2. The area of the bottom of the prism is 10 2 = 20 m 2. The surface area of the triangular prism is = 52 m 2. So, the surface area is = 192 m 2. Find the surface area of each figure. Show your work m 6 m 16 m 4 m 5 m 4. FLOWER BOX Find the surface area of the open-top flower box shown.

21 Extended Constructed Response Question Show your work & explain your answer. Look at the following expression (4 + 2) Part A What are the first two steps you would take to find the value of this expression? Explain. Part B Find the value of the expression. Be sure to rewrite the expression after each step.