Survey

Survey

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3.3 Problem Solving in Geometry Perimeter (Circumference), Area, and Volume Ex. Find the area: 26m 18m 18m 37m 21.1m A = ½h(a + b) A = ½(18)(26 + 37) A = ½(18)(63) A = 9(63) A = 567 The area is 567 m2 Ex. A rectangle has a width of 46cm and a perimeter of 208cm. What is its length? x = length width = 46 cm length = x P = 2L + 2W 208 = 2(x) + 2(46) 208 = 2x + 92 208 – 92 = 2x + 92 – 92 116 = 2x 116 = 2x 2 2 58 = x The length is 58 cm Circles diameter – distance across circle through the center d r radius – distance from center to edge of circle (half the diameter) Note: π is approximately 3.14 Ex. Find the area and circumference (a) in terms of π (b) rounded to the nearest whole number 9m A = πr2 A = π(9)2 A = π81 A = 81π (a) area is 81π m2 C = 2πr C = 2π(9) C = 18π (a) circumference is 18π m C = 18π C ≈ 18(3.14) A = 81π C ≈ 56.52 m A ≈ 81(3.14) (b) circumference is A ≈ 254.34 approximately 57 m (b) area is approximately 254 m2 Ex. A cylinder with radius 3 inches and height 4 inches has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder? Ex. A cylinder with radius 3 inches and height 4 inches has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder? 4in 4in 3in 9in V1 = πr2h V1 = π(3)2(4) V1 = π(9) (4) V1 = 36π in3 V2 = πr2h V2 = π(9)2(4) V2 = π(81) (4) V2 = 324π in3 9 V2 324 9 V1 36 1 9 times Ex. A water reservoir is shaped like a rectangular solid with a base that is 50 yards by 30 yards, and a vertical height of 20 yards. At the start of a three-month period of no rain, the reservoir was completely full. At the end of this period, the height of the water was down to 6 yards. How much water was used in the three-month period? Ex. A water reservoir is shaped like a rectangular solid with a base that is 50 yards by 30 yards, and a vertical height of 20 yards. At the start of a three-month period of no rain, the reservoir was completely full. At the end of this period, the height of the water was down to 6 yards. How much water was used in the three-month period? 20yd 6yd 30yd 50yd Vstart = lwh Vstart = (50)(30)(20) Vstart = 30,000 yd3 Vend = lwh Vend = (50)(30)(6) Vend = 9,000 yd3 Vstart – Vend = 30,000 – 9,000 = 21,000 yd3 Angles of a Triangle The sum of the interior angles of a triangle is 180°. C A B A° + B° + C° = 180° Ex. One angle of a triangle is three times as large as another. The measure of the third angle is 40°more than that of the smallest angle. Find the measure of each angle. Ex. One angle of a triangle is three times as large as another. The measure of the third angle is 40°more than that of the smallest angle. Find the measure of each angle. A° + B° + C° = 180° 3x x + 40 1 x 2 3x 3 x 40 x x + 3x + x + 40 = 180 5x + 40 = 180 5x + 40 – 40 = 180 – 40 5x = 140 5x = 140 5 5 x = 28 x = 28° 3x = 3(28) = 84° x + 40 = 28 + 40 = 68° 28°, 84°and 68° straight angle right angle 180° 90° complementary angles – 2 angles whose sum is 90° If one angle is x complementary angle is 90 – x B A A + B = 90° supplementary angles – 2 angles whose sum is 180° B A A + B = 180° angle 50° 17° x° comp 40° 73° (90 – x)° If one angle is x supplementary angle is 180 – x supp 130° 163° (180 – x)° Ex. Find the measure of an angle whose supplement measures 39° more than twice its complement. Ex. Find the measure of an angle whose supplement measures 39° more than twice its complement. angle = x comp = 90 – x supp = 180 – x 180 – x = 2(90 – x) + 39 180 – x = 180 – 2x + 39 180 – x = 219 – 2x 180 – x + 2x = 219 – 2x + 2x 180 + x = 219 180 + x – 180 = 219 – 180 x = 39 The angle is 39° Groups Page 212 – 213: 31, 47, 53, 61

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