Report

8.3 – Area, Volume and Surface Area Area of Plane Regions Rectangle Square 3 ft 2 ft 6 ft Triangle 3 ft A = l·w A = 6·2 A = s·s = s2 A = 32 A = 12 sq ft A = 9 sq ft 3 ft 4 ft A = ½ l·w A = ½ b·h A = ½ ·4·3 A = 6 sq ft 8.3 – Area, Volume and Surface Area Area of Plane Regions Triangle Parallelogram Trapezoid 8 cm 2m 4m 3 yd 7 yd A = ½ b·h A = ½ ·4·2 A = b·h A = 7·3 A = 4 sq m A = 21 sq yd 9 cm 12 cm A = ½ (b1 + b2)·h A = ½ (12 + 8)·9 A = ½ ·20·9 A = 90 sq cm 8.3 – Area, Volume and Surface Area Calculate the area of the plane region 24 m A = A + A 12 m 6m 18 m A = 12 · 6 + 18·18 A = 72 + 324 6m A = 396 sq m 18 m 24 – 18 = 6 m 18 – 12 = 6 m 8.3 – Area, Volume and Surface Area Area of Plane Regions Circle Exact Area A = ·r2 Approximate Area A = 3.14 ·r2 r d Calculate the area Exact Area r d Diameter = 14 inches r = 7 inches A = ·r2 A = ·72 A = 49 sq in Approximate Area A = 3.14 ·r2 A = 3.14 ·72 A = 3.14 ·49 A = 153.86 sq in 8.3 – Area, Volume and Surface Area Formulas for Volume and Surface Area 8.3 – Area, Volume and Surface Area Formulas for Volume and Surface Area 8.3 – Area, Volume and Surface Area Calculate the volume and surface area of a rectangular box (prism) that is 7 feet long, 3 feet wide and 4 feet high. V = l·w·h SA = 2lw + 2wh + 2hl V = 7·3·4 SA = 2(lw + wh + hl) V = 21·4 V = 84 cu ft SA = 2(7·3 + 3·4 + 4·7) SA = 2(21 + 12 + 28) SA = 2(21 + 40) SA = 2(61) SA = 122 sq ft 8.3 – Area, Volume and Surface Area Approximate the volume and surface area of a cylinder that has a radius of 5 inches and height of 9 inches. ( ≈ 3.14) V = · r2 · h SA = 2r2 + 2rh V = 3.14·52·9 SA = 2·3.14·52 + 2·3.14·5·9 V = 3.14·25·9 SA = 2·3.14·25 + 2·3.14·45 V = 3.14·225 SA = 50·3.14 + 90·3.14 V = 706.5 cu in SA = 3.14(50 + 90) SA = 3.14(140) SA = 439.6 sq in 8.3 – Area, Volume and Surface Area Calculate the volume of a square-base pyramid that has a base side measurement of 3 meters and a height of 5.1 meters. V = (1/3)· b2 · h V = (1/3)·32·5.1 V = (1/3)·9·5.1 V = 3·5.1 V = 15.3 m3 8.3 – Area, Volume and Surface Area Approximate the volume of a cone that has a radius of 4 yards and a height of 6 yards. Round the answer to the nearest tenth of a yard. Use 22/7 as the approximation of . V = (1/3) · r2 · h V = (1/3)(22/7)·42·6 V = (1/3)(22/7)·16·6 V = (22/7)·16·2 V = (22/7)·32 V = 704/7 V = 100.6 cu yd 8.4 – Linear Measurement U. S. Units of Length U. S. Unit Fractions 12 in 1 ft 12 in 3 ft 1 yd 1 ft 12 in 36 in 1 yd 3 ft 1 yd 5280 ft 1 mi 1 1 or or 1 ft 1 yd 3 ft 36 in 1 yd 1 or 1 yd 5 , 280 ft 1 mi 1 1 1 36 in 1 or 1 mi 5 , 280 ft 1 8.4 – Linear Measurement Conversions Convert 6 feet to inches. 6 ft x in Convert 8 yards to feet. 1 ft 8 yd 12 in x ft 1 yd 3 ft x 6 12 x 83 x 72 in x 24 ft 8.4 – Linear Measurement Conversions Convert 68 inches to feet Convert 5 yards 2 feet to and inches. feet. 68 in x ft 12 in 5 yd 1 ft x ft 12 x 68 68 x 12 x 5 ft 8 in 1 yd 3 ft x 53 x 15 5 yd 2 ft = 15 + 2 = 17 ft 8.4 – Linear Measurement Conversions Add 5 feet 8 inches to 8 feet 11 inches. 5 feet 8 inches 8 feet 11 inches 13 feet 0 inches 1 feet 7 inches 13 feet 19 inches 14 feet 7 inches 19 in x ft 12 in 1 ft 12 x 19 19 x 12 x 1 ft 7 in 8.4 – Linear Measurement Conversions Multiply 4 feet 7 inches by 4. 4 feet 7 inches × 4 16 feet 0 inches 2 feet 4 inches 16 feet 28 inches 18 feet 4 inches 28 in x ft 12 in 1 ft 12 x 28 28 x 12 x 2 ft 4 in 8.4 – Linear Measurement Conversions A carpenter cuts 1 ft 9 in from a board of length 5 ft 8 in. What is the length of the remaining piece. 5 feet 8 inches – 1 feet 9 inches 4 20 5 feet 8 inches – 1 feet 9 inches 3 feet 11 inches 3 ft 11 in 8.4 – Linear Measurement Metric Units of Length Metric Unit Fractions 1000 m 1 km 1 km 100 cm 1 m 1000 m 1 km 10 mm 1 cm 1m 100 cm 1000 mm 1 m 1 1 or or 100 cm 1 cm 1000 mm 1 1 1m 1 or 10 mm 1m 1000 m 10 mm 1 1 cm 1 or 1000 mm 1m 1 8.4 – Linear Measurement Conversions Convert 2.5 m to millimeters. Convert 3500 m to km. 2 .5 m x mm 1m 3500 m 1000 mm x km x 2 . 5 1000 x 2 , 500 mm 1000 m 1 km 1000 x 3500 x 3500 1000 x 3 . 5 km 8.4 – Linear Measurement Conversions Subtract 21 mm from 6.4 cm. 6 . 4 cm x mm 1 cm 21 mm 10 mm x cm x 6 . 4 10 x 64 10 mm 1 cm 10 x 21 x 21 10 64 – 21 43 43 mm 6.4 – 2.1 4.3 4.3 cm x 2 .1 8.4 – Linear Measurement Conversions Multiply 18.3 cm by 6.2 and convert the answer to meters. 18.3 × 6.2 366 1098 11346 113.46 cm 113 . 46 cm 100 cm xm 1m 100 x 113 . 46 x 113 . 46 100 x 1 . 1346 m 8.4 – Linear Measurement Conversions A knitted scarf is currently 0.8 m long. If an additional 45 cm is knitted, how long will the scarf be? 0 .8 m x cm 1m 45 cm 100 cm xm x 0 . 8 100 x 80 80 + 45 125 125 cm 100 cm 1m 100 x 45 x 45 100 0.80 + 0.45 1.25 1.25 m x 0 . 45