The Pythagorean Theorem Problema and Answers

Section 2.1: The Pythagorean Theorem Homework #1-20: Use the Pythagorean Theorem to find the missing length. Round to two decimal places when necessary. Make sure to use units in your answer when the lengths are given with units. 1) 2) 3) 4) 5) Round your answer to 2 decimals. 6) 7) Find the length of the diagonal. Round your answer to 2 decimals. 8) Find the length of the diagonal. Round to 2 decimals. Section 2.1 continued: 9) Find the length of the diagonal. 10) Find the length of the diagonal. 11) Solve for x. Assume the units 12) Find the height of the are in meters. Round to 2 triangle. Assume the lengths are decimals. given in meters. 13) Find d and D. Round to 2 decimals. Hint the “ ‘ “ means the units are in feet. 15) Solve for c and d. 14) Find the lengths of the dashed lines. Assume sides are measured in feet. 16) Find d. Answers: 1) 13 cm 3) x = 45 cm 5) a = 8.94 in 7) 14.14 m 9) 40.25 m 11) 10.91 m 13) d = 12.73’ D = 15.59’ 15) c = 10 in d = 14.14 in Section 2.2: Perimeter and Area Homework #1-4: Find the circumference of each circle. Make sure to include the proper units in your answer. Leave your answer in terms of 𝜋𝜋. 1) 2) 3) 4) Homework #5-12: Find the perimeter. 5) 6) Section 2.2 Continued 7) Assume opposite sides have equal lengths. 8) Assume opposite sides have equal lengths. 9) 10) 11) 12) Homework: #13 – 24 Find the area of each figure. Use appropriate units. 13) Assume the lengths are in inches. 14) Section 2.2 Continued: 15) 16) 17) Find “a”, then find the area of the triangle. Assume lengths are given in inches. 18) Find “a”, then find the area of the triangle. Assume lengths are given in inches. 19) Find “t”, then find the area of the triangle. Assume lengths are given in centimeters. 20) Find “b”, then find the area of the triangle. Assume lengths are given in centimeters. 21) 22). Section 2.2 Continued: 23) 24) 25) 26) 27) 28) 29) 30) Section 2.2 Coninued: 31) 32) 33) Assume units are given in inches. 34) 35) 36) 37) 38) Section 2.1 Continued: 39) 40) Homework #41-56: Find the area of the shaded region. Use appropriate units. 41) Use 3.14 for 𝜋𝜋 42) 43) Leave your answer in terms of 𝜋𝜋. Assume measurements are given in feet. 44) Leave your answer in terms of 𝜋𝜋 Section 2.2 Continued: 45) Use 3.14 for 𝜋𝜋. Assume measurements are given in meters. 46) Find the length of the diagonal “d”, then find the shaded area. Use 3.14 for 𝜋𝜋. Assume measurements are given in meters. 47) Find the length of the diagonal “d” rounded to 2 decimals. Use “d” to find the radius. Round the radius to 2 decimals. Then find the shaded area. Use 3.14 for 𝜋𝜋. Assume measurements are given in meters 48) Find the length of the diagonal “d” rounded to 2 decimals. Use “d” to find the radius. Round the radius to 2 decimals. Then find the shaded area. Use 3.14 for 𝜋𝜋. Assume measurements are given in meters 49) 50) Assume units are in centimeters. Section 2.2 Continued: 51) 52) 53) Use 3.14 for 𝜋𝜋. Assume lengths are given 54) Use 3.14 for 𝜋𝜋. Round your answer to 2 in centimeters. Round your answer to 2 decimals. decimals. Section 2.2 Answers: 1) 28𝜋𝜋 𝑚𝑚 3) 16𝜋𝜋 𝑐𝑐𝑐𝑐 5) 24 cm 7) 28 cm 9) 436 ft 11) 20 in 13) 225 square inches 15) 70 m2 17) a= 7, area = 84 square inches 19) t = 5, area = 30 cm2 21) 30 cm2 23) 63.86 cm2 25) 109.18 square meters 27) 130 cm2 29) 18 m2 31) 144 square centimeters 33) 64 square inches 35) 16𝜋𝜋𝑐𝑐𝑐𝑐2 37) 9𝜋𝜋𝑖𝑖𝑖𝑖2 39) 64𝜋𝜋𝑐𝑐𝑐𝑐2 41) 165.76 cm2 43) 75𝜋𝜋𝑓𝑓𝑓𝑓 2 45) 29.5 m2 47) d = 2.83 m, r = 1.42 m area = 2.33 m2 (your answer will be different if you round different than the instructions) 49) 200 mm2 51) 208 cm2 53) 30.96 cm2 Section 2.3 Volume Homework # 1- 30: Find the volume. Leave your answer in terms of 𝜋𝜋 when appropriate. 1) 2) 3) 4) Assume measurements are in feet. 5) 6) 7) 8) Section 2.3 Continued: 9) 10) 11) Assume measurements are in centimeters. 12) 13) Assume the base of the pyramid is a square. Leave your answer in fraction form. 14) Assume that the units are given in meters. Round your answer to 2 decimals, if appropriate. Section 2.3 Continued: 15) This is a square pyramid. The base is a 4 cm by 4 cm square. 16) 17) 18) 19) Write your answer as a fraction in terms of 𝜋𝜋. 20) Write your answer as a fraction in terms of 𝜋𝜋. 21) Write your answer as a fraction in terms of 𝜋𝜋. 22) Write your answer as a fraction in terms of 𝜋𝜋. 23) Hint you will need to subtract to find the height of the cone. Write your answer as a fraction in terms of 𝜋𝜋. 24) Write your answer as a fraction in terms of 𝜋𝜋. 25) Write your answer in terms of 𝜋𝜋. 26) Write your answer as a fraction in terms of 𝜋𝜋. Section 2.3 Continued: 27) 28) Assume lengths are given in feet. 29) 30) Assume lengths are given in inches. 31) 32) Section 2.3 Answers: 1) 194.4 cm3 3) 36 ft3 5) 192𝜋𝜋 cm3 7) 4.608𝜋𝜋 ft3 9) 96𝜋𝜋 cm3 11) 175 10976 32 960𝜋𝜋 cm3 13) 3 m3 15) 48 cm3 17) 112 in3 19) 3 𝜋𝜋 m3 21) 3 𝜋𝜋 in3 23) 60840𝜋𝜋 ft3 25) 475 3 𝜋𝜋 cm3 27) 24000 ft3 29) 1428 in3 31) 24000 mm3 Section 2.4 Dimensional Analysis We will need to know a few equivalencies to do the problems in this section. I will give you all equivalencies from this list that you need on the test. There is no need to memorize these formulas. Length Volume Area 1 in = 2.54 cm 1 tsp = 5 ml 1 in2 = 6.5 cm2 1 ft = 30 cm 1 tbsp = 15 ml 1 ft2 = 0.09 m2 1 yd = 0.9 m 1 fl oz = 30 ml 1 yd2 = 0.8 m2 1 mi = 1.6 km 1 cup = 0.24 l 1 mi2 = 2.6 km2 1 ft = 12 in 1 pint = 0.47 l 1 yd = 3 ft 1 qt = 0.95 l 1 mi = 5280 ft 1 gal = 3.8 l 1 ft3 = 0.03 m3 Weight 1 yd3 = 0.76 m3 1 oz = 28 g 1 cup = 8 oz 1 lb = 0.45 kg 1 pint = 2 cups 1 Ton = 0.9 t (tonne) 1 quart = 2 pints 1 lb = 16 oz 3 7.48 gallons = 1 ft 1 ton = 2000 lb Metric Length millimeter centimeter 1000 (mm) 100 (cm) decimeter 10 (dm) meter 1 (m) dekameter 0.1 (dam) hectometer 0.01 (hm) kilometer 0.001 (km) Metric Weight milligram centigram 1000 (mg) 100 (cg) decigram 10 (dg) gram 1 (g) dekagram 0.1 (dag) hectogram 0.01 (hg) kilogram 0.001 (kg) Metric Volume milliliter centiliter 1000 (ml) 100 (cl) deciliter 10 (dl) liter 1 (l) dekaliter 0.1 (dal) hectoliter 0.01 (hl) kiloliter 0.001 (kl) #1-30: Use dimensional analysis to find the missing quantity. Round to 2 decimals when appropriate. 1) 10 m = _____cm 2) 500 ml = ____ l 3) 45 mg = _____ g 4) 20 kl = ____ l 5) 5 kl = ______ l 6) 8 kg = _____ g 7) 0.25 kl = ____cl 8) 50 dm = _____ dam 9) 5 ft = ____ in 10) 6 ft = ____ cm 11) 3 mi = ____ ft 12) 4 yd = ____ m Section 2.4 Continued: 13) 4 l = ____ cups 14) 40 oz = ____ cups 15) 3 fl oz = ____ l 16) 8 fl oz = ____ l 17) 400 oz = ____ kg 18) 6 kg = ____ oz 19) 10000 oz = ____ tons 20) 300 yd = ____ km 21) 21 l = ____ fl oz 22) 6 l = ____ fl oz 23) 10 kg = ____ oz 24) 220 oz = ____ kg 25) 3 tons = ____ oz 26) 2 km = ____ yd 27) 10 cups = ____ quarts 28) 8 quarts = ____ cups 29) 100 tsp = ____ l 30) 2 l = ____ tsp Homework # 31 – 50: Solve, round to 2 decimals when appropriate. 31) The distance from Cincinnati, Ohio to Columbus, Ohio is about 110 miles. What is the distance in kilometers? 32) The distance from Phoenix to Flagstaff is about 140 miles. What is the distance in kilometers? 33) Two cities 400 km apart. How many miles are they apart? 34) Two cities 1000 km apart. How many miles are they apart? 35) A swimming pool holds 12,500 gallons of water. How many cubic feet of water does it hold? (round to 2 decimals) 36) A bath tub holds 50 gallons of water. How many cubic feet of water does it hold? (round to 2 decimals) 37) A pool is 20 ft long, 15 ft wide and 4 ft deep. a) What is the volume of the pool in cubic feet? b) How many gallons of water can it hold? 38) A pool is 25 ft long, 18 ft wide and 5 ft deep. a) What is the volume of the pool in cubic feet? b) How many gallons of water can it hold? Section 2.4 Continued: 39) Consider the cylinder below. a) What is the volume of the cylinder? b) How many gallons of water can it hold? (Leave your answer in terms of 𝜋𝜋. 40) Consider the cone below. a) What is the volume of the cylinder? b) How many gallons of water can it hold? 41) Consider the figure below. a) What is the volume of the shape? b) How many gallons of water can it hold? (use 3.14 for 𝜋𝜋 and round your answer to 2 decimals.) Section 2.4 Continued: 42) Consider the figure below. a) What is the volume of the shape? b) How many gallons of water can it hold? 43) Part of the Queen Elizabeth Way in Canada has a speed limit of 80 kph. What is the speed limit in mph? 44) The speed limit on much of I-17 is 75 miles per hour. What is the speed in kilometers per hour? 45) One gram is the same as 5 carats. David’s new ring contains a precious stone that is 2 carats. Find the weight of the stone in grams. 46) One gram is the same as 5 carats. David’s new ring contains a precious stone that is 1/8 carat. Find the weight of the stone in grams. Answers: 1) 1000 cm 3) 0.045 g 5) 5,000 l 7) 25,000 cl 9) 60 in 11) 15,840 ft 2 13) 16 3 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 15) 0.09 l 17) 11.2 kg 19) .3125 T 21) 700 𝑓𝑓𝑓𝑓 𝑜𝑜𝑜𝑜 23) 357.14 oz 25) 96,000 oz 27) 2.5 qt 29) 0.5 l 31) 176 km 33) 250 mi 35) 1671.12 ft3 37a) 1200 ft3 37b) 8976 gallons 39a) 4.608𝜋𝜋 ft3 39b) 34.46784𝜋𝜋 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 41a) 60840𝜋𝜋 𝑓𝑓𝑓𝑓 3 41b) 1,428,961.25 gallons 43) 50 miles 45) 2/5 gram or 0.40 gram Section 2.5 Roman Numerals Homework: #1-28 Write as a Hindu Arabic numeral. 1) CCXLII 2) DXLVI 3) CDXLVII 4) CDXXXIV 5) LXXXVI 6) LXXVII 7) CXXIII 8) CXXXI 9) XLIX 10) XLIV 11) DCXVI 12) DCCLXVI 13) XXXIV 14) XXXIX 15) XCIX 16) XCIV 17) MCMXXX 18) MCMXCIII 19) MMCMIV 20) MMCMXCV 21) MMXIV 22) MMXIX 23) CMXCVII 24) CMXLVII 25) DCXLVII 26) DCCXLIX 27) CDLVI 28) CDXLVII Homework: # 29 – 60 Write as a Roman numeral. 29) 53 30) 57 31) 18 32) 17 33) 125 34) 131 35) 316 36) 722 37) 19 38) 29 39) 34 40) 24 41) 49 42) 44 43) 47 44) 48 45) 95 46) 98 47) 432 48) 446 49) 951 50) 957 51) 948 52) 941 53) 1950 54) 1973 55) 1994 56) 1999 57) 2016 58) 2019 59) 2024 60) 2043 Section 2.5 Answers: 1) 242 3) 447 5) 86 7) 123 9) 49 11) 616 13) 34 15) 99 17) 1930 19) 2904 21) 2014 23) 997 25) 647 27) 456 29) LIII 31) XVIII 33) CXXV 35) CCCXVI 37) XIX 39) XXXIV 41) XLIX 43) XLVII 45) XCV 47) CDXXXII 49) CMLI 51) CMXLVIII 53) MCML 55) MCMXCIV 57) MMXVI 59) MMXXIV Section 2.6 Homework #1-20: Convert to base 10 (some of your answers may be very large) 1) 2134 2) 2135 3) 316 4) 314 5) 101112 6) 1100112 7) 12347 8) 12346 9) 4135 10) 7128 11) 12245 12) 32157 13) 111012 14) 111013 15) 10415 16) 21046 17) 10023 18) 20013 19) 20234 20) 20314 Homework #21 – 40: Convert to the indicated base. 21) 43 to base 5 22) 56 to base 5 23) 213 to base 3 24) 315 to base 3 25) 73 to base 2 26) 53 to base 2 27) 37 to base 2 28) 41 to base 2 29) 313 to base 4 30) 72 to base 5 31) 49 to base 6 32) 5120 to base 8 33) 2143 to base 5 34) 3120 to base 3 35) 143 to base 4 36) 123 to base 2 37) 412 to base 2 38) 914 to base 3 Section 2.6 Answers: 1) 39 3) 19 5) 23 7) 466 9) 108 11) 189 13) 29 15) 146 17) 29 19) 139 21) 1335 23) 212203 25) 10010012 27) 1001012 29) 103214 31) 1216 33) 320335 35) 20334 37) 1100111002