Warm UP Name the base, Name the figure 1. 2. 3 4. One square base; square pyramid Two pentagon bases, pentagonal prism Rectangular base, rectangular prism Two triangular bases, triangular prism
Area, Surface Area, and Volume Review Quiz Tomorrow!
Additional Example 1: Finding the Perimeter of a Polygon Find the perimeter. 25 cm 25 cm 15 cm P = 25 + 25 + 15 Use the side lengths. P = 65 Add. The perimeter of the triangle is 65 cm.
The perimeter of the rectangle is 64 ft. Additional Example 2: Using Properties of a Rectangle to Find Perimeter Find the perimeter of a rectangle. 14 ft 18 ft P = 2l + 2w Use the formula. P = (2 · 18) + (2 ·14) Substitute for l and w. P = 36 + 28 Multiply. P = 64 Add. The perimeter of the rectangle is 64 ft.
Additional Example 3A: Finding the Circumference of a Circle Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = d You know the diameter. 12 in. C 3.14 · 12 Substitute for and d. C 37.68 Multiply. The circumference of the circle is about 37.7 in.
Additional Example 3B: Finding the Circumference of a Circle Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = 2r You know the radius. 18 cm C 2 · 3.14 · 18 Substitute for and r. C 113.04 Multiply. The circumference of the circle is about 113.0 cm.
Additional Example 1A: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 Use the formula. 7 cm A 3.14 · 72 Substitute 7 for r. A 3.14 · 49 Evaluate the power. A 153.86 Multiply. The area of the circle is about 153.9 cm2. The order of operations calls for evaluating the exponents before multiplying. Remember!
Additional Example 1B: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 Use the formula. 18 ft A 3.14 · 92 Substitute 9 for r. A 3.14 · 81 Evaluate the power. A 254.34 Multiply. The area of the circle is about 254.3 ft2.
Find the area of the circle to the nearest tenth. Use 3.14 for . Check It Out: Example 1A Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 Use the formula. 10 cm A 3.14 · 102 Substitute 10 for r. A 3.14 · 100 Evaluate the power. A 314 Multiply. The area of the circle is about 314 cm2.
Find the area of the circle to the nearest tenth. Use 3.14 for . Check It Out: Example 1B Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 Use the formula. 12 ft A 3.14 · 62 Substitute 6 for r. A 3.14 · 36 Evaluate the power. A 113.04 Multiply. The area of the circle is about 113.0 ft2.
Additional Example 2: Finding the Area of an Irregular Figure Find the area of the irregular figure. Use 3.14 for . Step 1: Separate the figure into smaller, familiar figures. 16 m Step 2: Find the area of each smaller figure. 9 m Area of the parallelogram: 16 m A = bh Use the formula for the area of a parallelogram. A = 16 • 9 Substitute 16 for b. Substitute 9 for h. A = 144
Lesson Quiz Find the perimeter and area of each figure. 1. 2. 31.42 cm, 62.13 cm2 39.1 ft, 84 ft2
Check It Out: Example 1B Find the volume of the figure to the nearest tenth. Use 3.14 for . B = (82) Area of base 8 cm = 64 cm2 V = Bh Volume of a cylinder 15 cm = (64)(15) = 960 3,014.4 cm3
Check It Out: Example 1C Find the volume of the figure to the nearest tenth. Use 3.14 for . B = • 12 • 10 1 2 Area of base 10 ft = 60 ft2 V = Bh Volume of a prism 14 ft = 60(14) = 840 ft3 12 ft
Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for . 10 in. 1. 2. 3. 2 in. 12 in. 12 in. 10.7 in. 15 in. 3 in. 8.5 in. 942 in3 306 in3 160.5 in3 .
Lesson Quiz for Student Response Systems 1. Identify the volume of the cylinder to the nearest tenth. Use 3.14 for . A. 1099 in3 B. 1582.6 in3 C. 1356.5 in3 D. 1846.3 in3 16
Lesson Quiz for Student Response Systems 2. Identify the volume of the rectangular prism to the nearest tenth. A. 338 m3 B. 390 m3 C. 364 m3 D. 422.5 m3 17
Check It Out: Example 1A Find the volume of the figure. Use 3.14 for p. B = (5 • 7) = 17.5 in2 1 2 7 in. 1 3 V = • 17.5 • 7 V = Bh 1 3 5 in. 7 in. V 40.8 in3
Check It Out: Example 1B Find the volume of the figure. Use 3.14 for p. B = (32) = 9 m2 7 m 1 3 V = • 9 • 7 V = Bh 1 3 3 m V = 21 65.9 m3 Use 3.14 for .
Lesson Quiz: Part I Find the volume of each figure to the nearest tenth. Use 3.14 for p. 1. the triangular pyramid 6.3 m3 2. the cone 78.5 in3
Lesson Quiz for Student Response Systems 1. Identify the volume of the triangular pyramid rounded to the nearest tenth. A. 16 m3 B. 16.5 m3 C. 17 m3 D. 17.5 m3 21
Lesson Quiz: Part I Find the volume of each sphere, both in terms of and to the nearest tenth. Use 3.14 for p. 1. r = 4 ft 2. d = 6 m Find the surface area of each sphere, both in terms of and to the nearest tenth. Use 3.14 for p. 85.3p ft3, 267.8 ft3 36p m3, 113.0 m3 3. r = 22 in 1936p in2, 6079.0 in2 4. d = 1.5 mi 2.25p mi2, 7.1 mi2
Lesson Quiz for Student Response Systems 1. Find the volume of a sphere with radius 5 ft, both in terms of p and to the nearest tenth. Use 3.14 for p. A. 166.7p ft3, 523.3 ft3 B. 166.7p ft3, 576.5 ft3 C. 183.6p ft3, 576.5 ft3 D. 183.6p ft3, 523.3 ft3 23
Lesson Quiz for Student Response Systems 2. Find the volume of a sphere with a diameter of 8 m, both in terms of p and to the nearest tenth. Use 3.14 for p. A. 682.7p m3, 2143.6 m3 B. 682.7p m3, 267.9 m3 C. 85.3p m3, 2143.6 m3 D. 85.3p m3, 267.9 m3 24
Lesson Quiz Find the surface area of each figure to the nearest tenth. 1. 2. 100.5 ft2 352 ft2 3. The jewelry box is a composite figure. What is its surface area to the nearest tenth? Use 3.14 for 117.7 in2
Lesson Quiz for Student Response Systems 1. Identify the surface area of the prism with dimensions 16 ft by 9 ft by 5 ft. A. 588 ft2 B. 538 ft2 C. 288 ft2 D. 240 ft2 26 26
Lesson Quiz for Student Response Systems 2. Identify the surface area of the cylinder with diameter 10 cm and height 22 cm to the nearest tenth. Use 3.14 for . A. 1657.9 cm2 B. 2417.8 cm2 C. 3530.7 cm2 D. 4835.6 cm2 27 27 27