CIRCUMFERENCE Lesson 8-1

Vocabulary Start-Up A circle is the set of all points in a plane that are the same distance from a point, called the center. The circumference is the distance around a circle. The diameter is the distance across a circle through its center. The radius is the distance from the center to any point on the circle. Fill in the box with one of the vocabulary terms.

Real-World Link The table shows the approximate measurements of two sizes of hula hoops. a. Describe the relationship between the diameter and radius of each hula hoop. The diameter is twice the radius b. Describe the relationship between the circumference and diameter of each hula hoop. The circumference is about three times the diameter.

Radius and Diameter

Example 1 & 2

Got it? 1 & 2 Find the radius or diameter for each circle with the given dimensions. a. d = 23 cmb. r = 3 inches c. d = 16 yardsd. r = 5.2 meters 11.5 cm6 inches 8 yards 10.4 meters

Circumference

Example 3

Got it? inches

Example 4

Got it? 4

AREA OF CIRCLES Lesson 8-2

Real-World Link 1. Adrianne wants to find the distance the dog runs when it runs one circle with the leash fully extended. Should she calculate the circumference or area? Explain. Circumference; the circumference is the distance around the circle 2. Suppose she wants to find the amount of running room the dog has with the leash fully extended. Should she calculate the circumference or area? Explain. Area; the area is the interior region of an enclosed figure

Find the Area of a Circle

Example 1

Example 2

Got it? 1 & 2 Find the area of a circle with a radius of 3.2 centimeters. Round to the nearest tenth cm 2

Example 3

Got it? 3 The bottom of a circular swimming pool with a diameter of 30 feet is painted blue. How many square feet are blue? Round to the nearest tenth ft 2

Example 4 – Area of Semicircles

Got it? 4 Find the approximate area of a semicircle with a radius of 6 centimeters. Round to the nearest tenth cm 2

Example 5

AREA OF COMPOSITE FIGURES Lesson 8-3

Find the Area of a Composite Figure A composite figure is made up of two or more shapes. To find the area of a composite figure, decompose the figure into shapes with areas you know. Then find the sum of these areas. ShapeFormula ParallelogramA = (base)(height) Triangle Trapezoid Circle

Example 1 Find the area of the composite figure. The figure can be separated into a semicircle and a triangle. The area of the figure is about or 47.1 square meters.

Got it? 1 Find the area of the figure. Round to the nearest tenth if necessary in 2

Example 2 A miniature gold hole is composed of a trapezoid and a parallelogram. How many square feet of turf does the hole cover? So, or 22.5 square feet of turf will be needed.

Got it? 2 Pedro’s father is building a shed. How many square feet of wood are needed to build the back of the shed shown? 210 ft 2

Example 3 – Find Area of Shaded Region Find the area of the rectangle and subtract the area of the four triangles. The area of the shaded region is 60 – 2 or 58 square inches.

Example 4 – Find Area of Shaded Region The blueprint for a hotel swimming area is represented by the figure shown. The shaded area represents the pool. Find the area of the pool. The area of the shaded region is 1,050 – 440 or 610 square meters.

Got it? 3 & 4 A diagram for a park is shown. The shaded area represented the picnic sections. Find the area of the picnic sections. 2,250 yd 2

VOLUME OF PRISMS Lesson 8-4

Volume of a Rectangular Prism

The volume of a three-dimensional figure is the measure of space it occupies. It is measured in cubic units such as centimeters (cm 3 ) or cubic inches (in 3 ). It takes 2 layers of 36 cubes to fill the box. So, the volume of the box is 72 cubic centimeters.

Example 1

Got it? 1 Find the volume of the rectangular prism shown below m 3

Volume of a Triangular Prism Words: The volume V of a triangular prism is the product of the base B times the height h. Symbols: V = Bh, where B is the area of the base Model:

Volume of a Triangular Prism The diagram below shows that the volume of a triangular prism is also the product of the area of the base B and the height h of the prism.

Example 2

Got it? 2 Find the volume of the triangular prism shown below. 70 in 3

Example 3 Which lunch box holds more food? Find the volume of each lunch box. Then compare. Since 285 in 3 > in 3, Lunch Box B holds more food.

VOLUME OF PYRAMIDS Lesson 8-5

Real – World Link Dion is helping his mother build a sand sculpture at the beach in the shape of a pyramid. The square pyramid has a base with length and width of 12 inches an d the height of 14 inches. 1. Label the dimensions of the sand sculpture on the square pyramid below. 2. What is the area of the base? 144 in 2 3. What is the volume of a square prims with the same dimensions? 2,016 in 3

Volume of a Pyramid VOCABULARY: In a polyhedron, any face that is not the base is called a lateral face. The lateral faces meet at a common point or vertex.

Example 1

Example 2

Got it? 1 & 2 Find the volume of a pyramid that has a height of 9 centimeters and a rectangular base with a length of 7 centimeters and a width of 3 centimeters. 63 cm 3

Example 3

Example 4

Got it? 3 & 4 a. A triangular pyramid has a volume of 840 cubic inches. It has a base of 20 inches and a height of 21 inches. Find the height of the pyramid. 12 inches b. A rectangular pyramid has a volume of 525 cubic feet. It has a base of 25 feet by 18 feet. Find the height of the pyramid. 3.5 feet

Example 5

SURFACE AREA OF PRISMS Lesson 8-6

Real-World Link Members of a local recreation center are permitted to post messages on 8.5-inch by 11-inch paper on the board. Assume the signs are posted vertically and do not overlap. 1. Suppose 6 messages fit across the board widthwise. What is the width of the board in inches? _______ inches 2. Suppose 3 messages fit down the board lengthwise. What is the length of the board in inches? _______ inches 3. What is the area in square inches of the message board? 1,683 in 2 4. What is the total area of the front and back of the board? 3,366 in

Surface Area of a Rectangular Prism

Example 1

Got it? 1 Find the surface area of each prism. a. b. 216 m mm 2

Example 2

Domingo built a toy box 60 inches long, 24 inches wide, and 36 inches high. He has 1 quart of paint that covers about 87 square feet of surface. Does he have enough to pain the toy box? Justify your answer. Find the number of square inches the paint will cover. 1 ft 2 = 1 ft x 1 ft = 12 in x 12 in = 144 in 2 So, 87 square feet is equal to 87 x 144 or 12,528 square inches. Since 12,528 > 8,928, Domingo has enough paint.

Got it? 2 The largest corrugated cardboard box ever constructed measured about 23 feet long, 9 feet high, and 8 feet wide. Would 950 square feet of paper be enough to cover the box? Justify your answer. Yes, the surface area of the box is 926 ft 2 and 950 ft 2 > 926 ft 2.

Surface Area of Triangular Prism 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 of the faces rather than using a formula.

Example 3

Got it? 3 Find the surface area of the triangular prism. 38 cm 2

SURFACE AREA OF PYRAMIDS Lesson 8-7

Vocabulary Start-Up A right square pyramid has a square base and four isosceles triangles that make up the lateral faces. The lateral surface area is sum of the areas of its lateral faces. The height of each lateral face is called the slant height. 1. Fill in the blanks. 2. Draw a net of a square pyramid.

Surface Area of a Pyramid

Surface Area of a Regular Pyramid

Example 1

Example 2

Example 3

Got it? 1 – 3 a. Find the surface area of a square pyramid that has a slant height of 8 centimeters and a base length of 5 centimeters. 105 cm 2 b. Find the total surface area of the pyramid m 2

Example 4

Got it? 4 Amado purchased a bottle of perfume that is in the shape of a square pyramid. The slant height of the bottle is 4.5 inches and the base is 2 inches. Find the surface area. 22 in 2

VOLUME AND SURFACE AREA OF COMPOSITE FIGURES Lesson 8-8

Example 1 Find the volume of the composite figure. Find the volume of each prism. The volume is or 1,152 cubic inches.

Example 2 Find the volume of the composite figure. Find the volume of each prism. The volume is or cubic feet.

Got it? 1 & 2 Find the volume of the composite figure. 228 cm 3

Example 3 Find the surface area of the composite figure. Find the surface area of each prism. Total Surface Area is 2(192) + 2(96) + 4(48) or 768 in 2.

Example 4 Find the surface area of the composite figure. Find the surface area of each prism. The surface area is 5(64) + 4(25.6) or square feet.

Got it? 3 & 4 Find the surface area of this composite figure. 30 ft 2