Mathematics Applications and Concepts Course 3 Interactive Chalkboard

Mathematics: Applications and Concepts, Course 3 Interactive Chalkboard Copyright © by The Mc. Graw-Hill Companies, Inc. Developed by FSCreations, Inc. , Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/Mc. Graw-Hill 8787 Orion Place Columbus, Ohio 43240

Lesson 7 -1 Area of Parallelograms, Triangles, and Trapezoids Lesson 7 -2 Circumference and Area of Circles Lesson 7 -3 Area of Complex Figures Lesson 7 -4 Three-Dimensional Figures Lesson 7 -5 Volume of Prisms and Cylinders Lesson 7 -6 Volume of Pyramids and Cones Lesson 7 -7 Surface Area of Prisms and Cylinders Lesson 7 -8 Surface Area of Pyramids and Cones Lesson 7 -9 Precision and Significant Digits

Example 1 Find the Area of a Parallelogram Example 2 Find the Area of a Triangle Example 3 Find the Area of a Trapezoid Example 4 Use Area to Solve a Real-Life Problem

Find the area of the parallelogram. The base is 7 centimeters. The height is 2 centimeters. Area of a parallelogram Replace b with 7 and h with 2. Multiply. Answer: The area is 14 square centimeters.

Find the area of the parallelogram. Answer:

Find the area of the triangle. The base is 22 inches. The height is 4 inches. Area of a triangle Replace b with 22 and h with 4.

Multiply. Answer: The area is 44 square inches.

Find the area of the triangle. Answer:

Find the area of the trapezoid. The height is 3. 4 yards. The lengths of the bases are 5 yards and 1 yard. Area of a trapezoid Replace h with 3. 4, and with 1. with 5,

or 10. 2 Simplify. Answer: The area of the trapezoid is 10. 2 square yards.

Find the area of the trapezoid. Answer:

PAINTING A farmer plans to paint the triangular side of a large shed, shown below. Find the area to be painted. (Assume that no part of the window needs to be painted. ) If a gallon of paint covers 350 square feet, how many gallons should the farmer buy? To find the area to be painted, subtract the area of the square from the area of the triangle.

Area of triangle Area of square or 387. 5 The area to be painted is 387. 5 – 9 or 378. 5 square feet. If one gallon of paint covers 350 square feet, then the farmer will need 378. 5 350 or about 1. 1 gallons. Since the farmer cannot buy a fraction of a gallon, he will need 2 gallons. Answer: 2 gallons

PAINTING Tyler plans to paint his front door, shown at the right. Find the area to be painted. (Assume that no part of the windows will be painted. ) If a quart of paint covers 50 square feet, how many quarts should Tyler buy? Answer: 1 qt

Example 1 Find the Circumferences of Circles Example 2 Find the Circumferences of Circles Example 3 Find the Areas of Circles Example 4 Find the Areas of Circles Example 5 Use Circumference and Area

Find the circumference of the circle. Round to the nearest tenth. Circumference of a circle Replace d with 5. This is the exact circumference. Use a calculator to find . 5 x ENTER 15. 70796327 Answer: The circumference is about 15. 7 feet.

Find the circumference of the circle. Round to the nearest tenth. Answer: 22. 0 in.

Find the circumference of the circle. Round to the nearest tenth. Circumference of a circle Replace r with 3. 8. Use a calculator. Answer: The circumference is about 23. 9 meters.

Find the circumference of the circle. Round to the nearest tenth. Answer: 22. 6 m

Find the area of the circle. Round to the nearest tenth. Area of a circle Replace r with 3. Evaluate Use a calculator. Answer: The area is about 28. 3 square yards.

Find the area of the circle. Round to the nearest tenth. Answer:

Find the area of the circle. Round to the nearest tenth. Area of a circle Replace r with half of 10 or 5. Evaluate Use a calculator. Answer: The area is about 78. 5 square inches.

Find the area of the circle. Round to the nearest tenth. Answer:

POOLS The Patels have a circular pool with a radius of 12 feet. They plan on installing a 4 -foot-wide walkway around the pool. What will be the area of the walkway? To determine the area of the walkway, you must subtract the area of the pool from the area of the outer circle that includes the pool and the walkway.

Area of Outer Circle Area of a circle Replace r with 12 Evaluate Use a calculator. 4 or 16.

Area of Pool Area of a circle Replace r with 12. Evaluate Use a calculator.

Area of Walkway Area of Outer Circle – Area of Pool Answer: The area of the walkway is about 351. 9 square feet.

GARDENS The Shoemakers have a circular pond with a radius of 4 feet. They plan on installing a 2 -foot-wide walkway around the pond. What will be the area of the walkway? Answer:

Example 1 Find the Area of a Complex Figure Example 2 Find the Area of a Complex Figure Example 3 Use the Area of a Complex Figure

Find the area of the complex figure. The figure can be separated into a rectangle and two congruent triangles.

Area of rectangle Area of one triangle 5 Answer: The area of the figure is square inches.

Find the area of the complex figure. Answer:

Find the area of the complex figure. Round to the nearest tenth. The figure can be separated into two semicircles and a rectangle.

Area of one semicircle Area of rectangle Answer: The area of the figure is about square centimeters.

Find the area of the complex figure. Round to the nearest tenth. Answer:

SHORT-RESPONSE TEST ITEM Below are plans for the new deck on the Obwena’s house. How many square feet of wood will be needed if one square represents two square feet? Read the Test Item You need to find the area of the deck in square units and then multiply this result by 2 to find the area of the deck in square feet.

Solve the Test Item Find the area of the deck by dividing it into smaller areas.

Region A Square or 4 Region B Triangle or 2 Region C Rectangle or 6

Region D Rectangle or 8 Region E Triangle Region F Rectangle

Region G Triangle Region H Square Answer: The total area is or square units. So, 2(36) or 72 square feet of wood is needed to make the deck.

SHORT-RESPONSE TEST ITEM Below are plans for the new patio to be added in the Murphy’s back yard. How many square feet of concrete will need to be poured if one square represents two square feet? Answer:

Example 1 Identify Prisms and Pyramids Example 2 Identify Prisms and Pyramids Example 3 Analyze Real-Life Drawings Example 4 Analyze Real-Life Drawings

Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: The figure has two parallel congruent bases that are octagons, so it is an octagonal prism. The other faces are rectangles. It has a total of 10 faces, 24 edges, and 16 vertices.

Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: triangular prism; 2 triangular faces, 3 rectangular faces, 9 edges, and 6 vertices

Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: The figure has one base that is a rectangle, so it is a rectangular pyramid. The other faces are triangles. It has a total of 5 faces, 8 edges, and 5 vertices.

Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: pentagonal pyramid; 1 pentagonal base, 5 triangular faces, 10 edges, and 6 vertices

ARCHITECTURE The plans for a hotel fireplace are shown below. Draw and label the top, front, and side views. Answer:

ARCHITECTURE The plans for a building are shown to the right. Draw and label the top, front, and side views. Answer:

ARCHITECTURE The plans for a hotel fireplace are shown to the right. Each unit on the drawing represents 1. 5 feet. Find the area of the floor covered by the fireplace. You can see from the front view that the floor is a rectangle that is 5 units wide by 6 units long. The actual dimensions are 5(1. 5) feet by 6(1. 5) feet or 7. 5 feet by 9 feet.

Simplify. Answer: The area of the floor covered by the fireplace is 67. 5 square feet.

ARCHITECTURE The plans for a building are shown at the right. Each unit on the drawing represents 150 feet. Find the area covered by the second floor. Answer:

Example 1 Find the Volume of a Rectangular Prism Example 2 Find the Volume of a Triangular Prism Example 3 Find the Volumes of Cylinders Example 4 Find the Volumes of Cylinders Example 5 Find the Volume of a Complex Solid

Find the volume of the prism. Volume of a prism The base is a rectangle, so Simplify. Answer: The volume is 385 cubic inches. .

Find the volume of the prism. Answer:

Find the volume of the prism. Volume of a prism The base is a triangle, so The height of the prism is 4. Simplify. Answer: The volume is 270 cubic inches.

Find the volume of the prism. Answer:

Find the volume of the cylinder. Round to the nearest tenth. Volume of a cylinder Replace r with 3 and h with 12. Simplify. Answer: The volume is about 339. 3 cubic centimeters.

Find the volume of the cylinder. Answer:

Find the volume of the cylinder. Round to the nearest tenth. diameter of base, 18 yd; height, 25. 4 yd Since the diameter is 18 yards, the radius is 9 yards. Volume of a cylinder Replace r with 9 and h with 25. 4. Simplify. Answer: The volume is about 6, 463. 5 cubic yards.

Find the volume of the cylinder. Round to the nearest tenth. diameter of base, 8 yd; height, 10 yd Answer:

TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. The block is a rectangular prism with a cylindrical hole. To find the volume of the block, subtract the volume of the cylinder from the volume of the prism.

Rectangular Prism Cylinder or 72 Answer: The volume of the box is about cubic centimeters.

HOBBIES A small wooden cube has been glued to a larger wooden block for a whittling project. What is the volume of the wood to be whittled? Answer:

Example 1 Find the Volume of a Pyramid Example 2 Use Volume to Solve a Problem Example 3 Find the Volume of a Cone

Find the volume of the pyramid. Volume of a pyramid Simplify. Answer: The volume is 140 cubic centimeters.

Find the volume of the pyramid. Answer:

SOUVENIRS A novelty souvenir company wants to make snow “globes” shaped like a pyramid. It decides that the most cost-effective maximum volume of water for the pyramids is 12 cubic inches. If a pyramid globe measures 4 inches in height, find the area of its base. Volume of a pyramid Replace V with 12 and h with 4.

Simplify. Answer: The area of the base of the snow globe is 9 square inches.

TOYS A company is designing pyramid shaped building blocks with a square base. They want the volume of the blocks to be 18 square inches. If the length of the side of the base is 3 inches, what should be the height of the blocks? Answer: 6 in.

Find the volume of the cone. Round to the nearest tenth. Volume of a cone Replace r with 1. 5 and h with 8. Simplify. Answer: The volume is about 18. 8 cubic meters.

Find the volume of the cone. Round to the nearest tenth. Answer:

Example 1 Surface Area of a Rectangular Prism Example 2 Surface Area of a Triangular Prism Example 3 Surface Area of a Cylinder

Find the surface area of the rectangular prism. Write the formula. Substitution. Simplify. Answer: The surface are is 606 square millimeters.

Find the surface area of the rectangular prism. Answer:

CAMPING A family wants to reinforce the fabric of its tent with a waterproofing treatment. Find the surface area, including the floor, of the tent below. A triangular prism consists of two congruent triangular faces and three rectangular faces.

Draw and label a net of this prism. Find the area of each face. bottom left side right side two bases Add to find the total surface area. Answer: The surface area of the tent is about 131. 1 square feet.

DECORATING Julia is painting triangular prisms to use as decoration in her garden. Find the surface area of the prism. Answer:

Find the surface area of the cylinder. Round to the nearest tenth. Surface area of a cylinder Replace r with 2. 5 and h with 2. Simplify. Answer: The surface area is about 70. 7 square meters.

Find the surface area of the cylinder. Round to the nearest tenth. Answer:

Example 1 Surface Area of a Pyramid Example 2 Surface Area of a Cone

Find the surface area of the triangular pyramid. Find the lateral area and the area of the base. Area of each lateral face Area of a triangle or 20 Replace b with 5 and h with 8.

There are 3 faces, so the lateral area is 3(20) or 60 square inches. Area of base Answer: The surface area of the pyramid is the sum of the lateral area and the area of the base, square inches.

Find the surface area of the square pyramid. Answer:

Find the surface area of the cone. Round to the nearest tenth. Surface area of a cone. Replace r with 1. 5 and Simplify. Answer: The surface are of the cone is about 28. 3 square meters.

Find the surface area of the cone. Round to the nearest tenth. Answer:

Example 1 Identify Precision Units Example 2 Identify Significant Digits Example 3 Identify Significant Digits Example 4 Add Measurements Example 5 Multiply Measurements

Identify the precision unit of thermometer. Answer: There are 5 spaces between each 10°mark, so the precision unit is of 10 degrees or 2 degrees.

Identify the precision unit of the ruler. Answer: inch

Determine the number of significant digits in the measure 5, 000 feet. Answer: 1 significant digit

Determine the number of significant digits in the measure 21. 0 miles. Answer: 3 significant digits

Determine the number of significant digits in the measure 315. 05 ounces. Answer: 5 significant digits

Determine the number of significant digits in the measure 35. 006 centimeters. Answer: 5 significant digits

MAIL Venita took four packages to the post office. They weighed 1. 27 pounds, 3. 45 pounds, 0. 524 pound, and 2. 7 pounds. Write the combined weight of her mail using correct precision. 1. 27 2 decimal places 3. 45 2 decimal places 0. 524 3 decimal places 1 decimal place The least precise measurement has 1 decimal place, so round the sum to 1 decimal place. 7. 944 Answer: The combined weight of the packages is about 7. 9 pounds.

DELI Veric bought 1. 5 pounds of turkey, 0. 75 pound of roast beef, 2. 4 pounds of ham, and 0. 5 pound of salami. Write the combined weight of the lunch meat that Veric bought using correct precision. Answer: 5. 2 lb

Use the correct number of significant digits to find the volume of the cylinder. Use 3. 14 for pi. Volume of a cylinder The height of the cylinder has the least number of significant digits, 2. Answer: Round the answer, 187. 0017188, so that it has 2 significant digits. The volume of the cylinder is about 190 cubic inches.

Use the correct number of significant digits to find the volume of the rectangular prism. Answer:

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