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Parents Pricing Home NSC Mathematical Literacy Measuring volume and capacity Ice is usually used in cool drinks to further cool them
Ice is usually used in cool drinks to further cool them - NSC Mathematical Literacy - Question 5 - 2023 - Paper 2 Question 5
View full question Ice is usually used in cool drinks to further cool them.
Ice can be made by freezing water in different shapes.
Cubes are the most common shape used to make ice.
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View marking scheme Worked Solution & Example Answer:Ice is usually used in cool drinks to further cool them - NSC Mathematical Literacy - Question 5 - 2023 - Paper 2
Determine the surface area of a cube Only available for registered users.
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To find the surface area of the cube, we will use the formula:
e x t S u r f a c e A r e a = 6 i m e s ( e x t s i d e l e n g t h ) 2 ext{Surface Area} = 6 imes ( ext{side length})^2 e x t S u r f a ce A re a = 6 im es ( e x t s i d e l e n g t h ) 2 Substituting the given side length:
e x t S u r f a c e A r e a = 6 i m e s ( 4.5 e x t c m ) 2 = 6 i m e s 20.25 e x t c m 2 = 121.5 e x t c m 2 ext{Surface Area} = 6 imes (4.5 ext{ cm})^2 = 6 imes 20.25 ext{ cm}^2 = 121.5 ext{ cm}^2 e x t S u r f a ce A re a = 6 im es ( 4.5 e x t c m ) 2 = 6 im es 20.25 e x t c m 2 = 121.5 e x t c m 2 Therefore, the surface area of the cube is 121.5 cm² .
5.2.1 Calculate the total mass (in kg) of a wall built with 60 big blocks of ice. Only available for registered users.
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Given that each block weighs 2 tons:
Total mass = Number of blocks × Mass of each block
Total mass = 60 blocks × 2 tons = 120 tons
Converting tons to kg:
e x t T o t a l m a s s = 120 e x t t o n s i m e s 1000 e x t k g / t o n = 120000 e x t k g ext{Total mass} = 120 ext{ tons} imes 1000 ext{ kg/ton} = 120000 ext{ kg} e x t T o t a l ma ss = 120 e x t t o n s im es 1000 e x t k g / t o n = 120000 e x t k g Thus, the total mass of the wall is 120000 kg .
5.2.2 Calculate the volume of the ice that was carved out. Only available for registered users.
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Given the volume of melted ice:
Volume = 38,500 cm³
Using the formula to calculate the volume of water:
e x t V o l u m e o f c a r v e d i c e = e x t v o l u m e i m e s 0.92 ext{Volume of carved ice} = ext{volume} imes 0.92 e x t V o l u m eo f c a r v e d i ce = e x t v o l u m e im es 0.92 Calculating:
e x t V o l u m e o f c a r v e d i c e = 38 , 500 e x t c m 3 i m e s 0.92 = 35 , 420 e x t c m 3 ext{Volume of carved ice} = 38,500 ext{ cm}^3 imes 0.92 = 35,420 ext{ cm}^3 e x t V o l u m eo f c a r v e d i ce = 38 , 500 e x t c m 3 im es 0.92 = 35 , 420 e x t c m 3 Hence, the volume of the ice that was carved out is 35,420 cm³ .
5.3.1 Determine, in nautical miles, the difference in the distances from Tokyo to Honolulu and from Washington to Anchorage. Only available for registered users.
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To find the difference:
Distance from Washington to Anchorage = 3,350 nautical miles
Distance from Tokyo to Honolulu = 2,607 nautical miles
Calculating the difference:
e x t D i f f e r e n c e = 3 , 350 e x t n m − 2 , 607 e x t n m = 743 e x t n m ext{Difference} = 3,350 ext{ nm} - 2,607 ext{ nm} = 743 ext{ nm} e x t D i ff ere n ce = 3 , 350 e x t nm − 2 , 607 e x t nm = 743 e x t nm Thus, the difference in distances is 743 nautical miles .
5.3.2 Convert, to kilometres, the distance from Berlin to Anchorage. Only available for registered users.
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Using the given distance in miles:
Distance = 3,950 miles
Conversion factor: 1 mile = 1.151 km
Calculating:
e x t D i s t a n c e i n k m = 3 , 950 e x t m i l e s i m e s 1.151 e x t k m / m i l e = 4 , 546.45 e x t k m ext{Distance in km} = 3,950 ext{ miles} imes 1.151 ext{ km/mile} = 4,546.45 ext{ km} e x t D i s t an ce inkm = 3 , 950 e x t mi l es im es 1.151 e x t km / mi l e = 4 , 546.45 e x t km Therefore, the distance from Berlin to Anchorage is approximately 4,546.45 km .
5.3.3 Cargo needs to be shipped from Los Angeles to Honolulu and then from Honolulu to Tokyo. Only available for registered users.
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To calculate the average speed of the ship:
Total distance from Los Angeles to Honolulu: 2,607 nautical miles
Time taken: 10 days
Convert time to hours:
10 e x t d a y s = 10 i m e s 24 e x t h o u r s / d a y = 240 e x t h o u r s 10 ext{ days} = 10 imes 24 ext{ hours/day} = 240 ext{ hours} 10 e x t d a ys = 10 im es 24 e x t h o u rs / d a y = 240 e x t h o u rs Average speed calculation:
ext{Average Speed} = rac{ ext{Distance}}{ ext{Time}} = rac{2,607 ext{ nm}}{240 ext{ hours}} ext{ nm/hour}
u
Calculating:
For the completion of the task, the estimated arrival time needs to be determined. After calculating, it is anticipated that the ship will arrive on 24 September at 16:00 hours in Tokyo.
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