Advanced Mensuration T Madas T Madas exa peta

Advanced Mensuration © T Madas

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exa peta tera giga E P T G mega M k kilo UNIT centi c milli m micro μ nano n pico p femto f atto a 1018 units 1015 units 1012 units 109 units 106 units 103 units 10 -2 of a unit 10 -3 of a unit 10 -6 of a unit 10 -9 of a unit 10 -12 of a unit 10 -15 of a unit 10 -18 of a unit For example: 2 Megawatts = 2, 000 kilowatts = 2, 000 watts 200, 000, 000 bytes = = 200, 000 kilobytes = 200, 000 megabytes = 200 gigabytes 153, 000 nanoseconds = = 153 microseconds = 0. 153 milliseconds = 0. 000153 seconds 2. 37 km = = 2, 370 m = 2, 370, 000 mm © T Madas

x 1000 x 1000 x 1000 x 1000 exa peta tera giga E P T G mega M k kilo UNIT centi c milli m micro μ nano n pico p femto f atto a ÷ 1000 ÷ 1000 ÷ 1000 ÷ 1000 © T Madas

Converting between units of area and volume © T Madas

1 mm 1 cm 2 cm a square centimetre How many mm 2 in a cm 2 ? © T Madas

1 mm 1 cm 2 = 100 How 1 cm many mm 2 mm in a 2 cm 2 ? © T Madas

3 cm a cubic centimetre 1 cm How many mm 3 in a cm 3 ? 1 mm 1 cm © T Madas

1 cm 3 = 1000 mm 3 1 mm 1 cm © T Madas

More Examples © T Madas

How many cm 2 in a square metre? 1 m = 100 cm 1 m 2 = 100 x 100 = 10, 000 cm 2 How many mm 2 in a square metre? 1 m = 1000 mm 1 m 2 = 1000 x 1000 =1000, 000 mm 2 How many mm 3 in a cubic metre? 1 m = 1000 mm 1 m 2 = 1000 x 1000 = 1, 000, 000 mm 3 How many m 2 in a square kilometre? 1 km = 1000 m 1 km 2 = 1000 x 1000 = 1, 000 m 2 © T Madas

Convert 3. 76 m 2 into cm 2 1 m = 100 cm 1 m 2 = 100 x 100 = 10, 000 cm 2 3. 76 m 2 = 3. 76 x 10000 = 37, 600 cm 2 Convert 1, 350, 000 cm 3 into m 3 1 m = 100 cm 1 m 3 = 100 x 100 = 1, 000, cm 3 1, 350, 000 cm 3 = 1, 350, 000 ÷ 1, 000 = 1. 35 m 3 Convert 60, 000 mm 2 into m 2 1 m = 1000 mm 1 m 2 = 1000 x 1000 = 1, 000, mm 2 60, 000 mm 2 = 60, 000 ÷ 1, 000 = 0. 06 m 2 © T Madas

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12 inches = 1 foot 3 feet = 1 yard How many square feet in a square yard? 9 1 feet yard 3 square foot 1 3 yard feet © T Madas

12 inches = 1 foot 3 feet = 1 yard How many square inches in a square foot? 144 1 inches foot 12 square inch 121 inches foot © T Madas

12 inches = 1 foot 1 feet yard 3 3 feet = 1 yard How many cubic feet in a cubic yard? 1 3 yard feet © T Madas

12 inches = 1 foot 3 feet = 1 yard How many cubic feet in a cubic yard? 27 1 feet yard 3 Cubic foot 1 3 yard feet © T Madas

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Number of people Population density = area Area Density Country Population (km 2) (Persons/km 2) 10, 096, 000 131, 957 75. 51 56, 107, 000 551, 000 101. 82 57, 436, 000 301, 225 190. 67 Which countries 30, 542 are most and 323. 36 9, 878, 000 least densely populated? 57, 218, 000 244, 755 233. 78 10, 372, 000 88, 500 117. 19 14, 846, 000 33, 929 437. 56 3, 515, 000 70, 282 50. 01 5, 135, 000 43, 076 119. 21 © T Madas

Spain Population: 39, 150, 000 Area: 492, 431 km 2 Calculate the population density of Spain as number of people per square kilometre. 39150000 Number of people = ≈ 79. 5 persons/km 2 P. D. = area 492431 © T Madas

Spain Population: 39, 150, 000 Area: 492, 431 km 2 How many m 2 correspond to every resident of Spain? How many m 2 in a square kilometre? 1 km = 1000 m 1 km 2 = 1000 x 1000 = 1, 000 m 2 492431 km 2 = 492431 x 1000000 = 492, 431, 000 m 2 492, 431, 000 39, 150, 000 ≈ 12587 m 2 person © T Madas

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Average Speed = distance time The diagram below shows the distances between 3 towns A, B and C. A car took 1½ hours to travel from A to B and 1 hour from B to C. A B 78 miles 1½ hours C 47 miles 1 hour What is the average speed for the journey from A to B ? Av. Speed = 78 distance = = 52 mph 1. 5 time © T Madas

Average Speed = distance time The diagram below shows the distances between 3 towns A, B and C. A car took 1½ hours to travel from A to B and 1 hour from B to C. A B 78 miles 1½ hours C 47 miles 1 hour What is the average speed for the journey from B to C ? Av. Speed = distance = time 47 = 47 mph 1 © T Madas

Average Speed = distance time The diagram below shows the distances between 3 towns A, B and C. A car took 1½ hours to travel from A to B and 1 hour from B to C. A B 78 miles 1½ hours C 47 miles 1 hour What is the average speed for the journey from A to C ? Av. Speed = 125 distance = = 50 mph 2. 5 time © T Madas

Average Speed = distance time s= d t d s t d = 80 x 3. 75 c c A car travelled for 3¾ hours at an average speed of 80 km per hour. How far did it travel? d= s x t d = 300 km © T Madas

Average Speed = distance time d s= d t s t t= d s c t = 70 c A cyclist travelled for 70 km at an average speed of 40 km per hour. How many hours did he travel for? 40 t = 1. 75 hrs = 1 hour 45 min © T Madas

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An aeroplane covers a distance of 2080 km in 3 hours and 15 minutes. Calculate its average speed: a. in km/h b. in m/s 2080 distance Speed = = = 640 km/h 3. 25 time 2080 x 1000 distance 2080000 Speed = = = ≈ 178 m/s 3. 25 x 3600 time 11700 © T Madas

Average Speed = Some common distance time units m/s ms-1 km/h kmh-1 km/s kms-1 cm/s cms-1 mm/s mms-1 of speed The official S. I. unit © T Madas

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mass density = volume density is mass per unit volume The following cm 3 are made of different substances granite 5. 2 g wood 0. 92 g iron 7. 86 g copper gold marble 8. 93 g 19. 3 g 3. 2 g 1 cm 3 of water = 1 gram © T Madas

A certain Buddha statuette can be bought in solid bronze, silver or gold cast, all having identical volume but different masses. The following table shows some of the data about the statuette. Complete this table of data Mass (grams) 504 675 Volume (cm 3) m d= v m = dv 18. 5 c mass volume 8. 4 c density = c Density (g/cm 3) v= m d v © T Madas

A certain Buddha statuette can be bought in solid bronze, silver or gold cast, all having identical volume but different masses. The following table shows some of the data about the statuette. Complete this table of data Mass (grams) 504 675 Volume (cm 3) Density (g/cm 3) m d= v 8. 4 m = dv 18. 5 m v= d © T Madas

A certain Buddha statuette can be bought in solid bronze, silver or gold cast, all having identical volume but different masses. The following table shows some of the data about the statuette. Complete this table of data Mass (grams) 504 675 Volume (cm 3) 60 60 Density (g/cm 3) 8. 4 m d m = dv c v= 18. 5 v= 504 8. 4 m v= d c m d= v 60 v = 60 cm 3 © T Madas

A certain Buddha statuette can be bought in solid bronze, silver or gold cast, all having identical volume but different masses. The following table shows some of the data about the statuette. Complete this table of data Mass (grams) 504 675 Volume (cm 3) 60 60 60 Density (g/cm 3) 8. 4 11. 25 18. 5 m v d= m = dv 675 60 c d= c m d= v m v= d d = 11. 25 g/cm 3 © T Madas

A certain Buddha statuette can be bought in solid bronze, silver or gold cast, all having identical volume but different masses. The following table shows some of the data about the statuette. Complete this table of data Mass (grams) 504 675 1110 Volume (cm 3) 60 60 60 Density (g/cm 3) 8. 4 11. 25 18. 5 m = dv m = 60 x 18. 5 m v= d c m = dv c m d= v m = 1110 g © T Madas

A cast iron rod 1. 6 metres long has a cross sectional area of 8 cm 2. The mass of the rod is 9. 28 kg. Calculate: a. The volume of the metal in the rod b. The density of cast iron in g/cm 3 160 cm 8 cm 2 8 x 160 = 1280 cm 3 9. 28 x 1000 9280 mass = 7. 25 g/cm 3 = = density = volume 1280 © T Madas

Gold has a density of 21. 4 grams per cm 3. What is the density of gold in kg per m 3 ? 21. 4 ÷ 1000 0. 0214 mass = 21400 kg/m 3 = = density = volume 1 ÷ 1000000 0. 000001 How many grams in kilogram? How many cm 3 in a cubic metre? 1 m = 100 cm 1 m 2 = 100 x 100 = 1, 000 cm 3 21. 4 ÷ 1000 = 1 ÷ 1000000 21. 4 1000 1 1000000 = 21. 4 x 1000000 1 x 1000 = 21400 kg/m 3 © T Madas

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