Percentages and ratio · Ages 13–14

Density, pressure and exchange rates worksheet

Part of: Rates, ratios & proportions

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Percentages and ratio · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A district has an area of 44 km² and a population of 52800. Its population density =
Answer:
2.A block has a mass of 2370 g and a volume of 300 cm³. Its density =
Answer:
3.One day, 100 Hong Kong dollars buy 1890 yen. 2200 Hong Kong dollars buy yen, and 945 yen buy Hong Kong dollars.
Fill in each blank
Answer:
4.A box weighs 2975 N and its base has an area of 0.2 m². Standing on the floor, the pressure it puts on the floor =
Answer:
5.A material has a density of 2.5 g/cm³. What is the mass, in kg, of a block of it 3600 cm³ in volume?
Answer:
6.An empty tank is a cuboid 120 cm long, 40 cm wide and 70 cm high. A hose lets in 8 L of water a minute. How many minutes does it take to fill?
Answer:
7.19.3 g/cm³ = kg/m³
Answer:
8.May takes 3200 Hong Kong dollars to Taiwan; one day, 1 Hong Kong dollar buys 4.2 New Taiwan dollars. May changes it all and spends 11550 New Taiwan dollars, leaving New Taiwan dollars, worth Hong Kong dollars at the same rate.
Fill in each blank
Answer:

9.One day, 1 pound buys 9.7 Hong Kong dollars. How many Hong Kong dollars do 430 pounds buy?
- A. About 443.3 Hong Kong dollars
- B. 439.7 Hong Kong dollars
- C. 4171 Hong Kong dollars
- D. 417.1 Hong Kong dollars
Choose the right answer
Answer:
10.One day, 1 pound buys 9.7 Hong Kong dollars. How many Hong Kong dollars do 160 pounds buy?
- A. About 164.9 Hong Kong dollars
- B. 169.7 Hong Kong dollars
- C. 1552 Hong Kong dollars
- D. 155.2 Hong Kong dollars
Choose the right answer
Answer:
11.A hose lets in 15 L of water a minute. Filling an empty tank that holds 1.2 m³ takes 8 minutes.
True or false?
Answer:
12.The same headphones cost 510 Hong Kong dollars in Hong Kong and 8955 yen in Japan. One day, 100 Hong Kong dollars buy 1990 yen. Leaving other costs aside, where are they cheaper?
- A. They can't be compared
- B. In Japan
- C. In Hong Kong
- D. The same in both
Choose the right answer
Answer:

13.A district covers about 6.2 km², with a population density of about 60000 people per km². About how many people live there?
Working:
Answer:
14.A brick weighing 27 N puts more pressure on the ground resting on a face of 200 cm² than on a face of 100 cm².
True or false?
Working:
Answer:
15.A pool is a cuboid 5 m long, 3 m wide and 1.5 m deep. A pipe lets in 100 L of water a minute. The pool holds L, and filling it from empty takes minutes.
Fill in each blank
Working:
Answer:
16.A crown has a mass of 849.2 g. Lowered into a container full to the brim, it spills 52 cm³ of water: that is its volume. Pure gold has a density of 19.3 g/cm³. Were the crown pure gold, its volume would be cm³; it is cm³ more, so it isn't pure gold.
Fill in each blank
Working:
Answer:
17.Ka-yan wants to change 4400 Hong Kong dollars into yen. Shop A: 100 Hong Kong dollars buy 1900 yen, no fee. Shop B: 100 buy 1980 yen, but a fee of 50 Hong Kong dollars comes off first, and the rest is changed. Which shop gives more yen?
- A. Shop A
- B. They give the same
- C. Shop B
- D. They can't be compared
Choose the right answer
Working:
Answer:
18.A brick weighing 53 N puts more pressure on the ground resting on a face of 50 cm² than on a face of 100 cm².
True or false?
Working:
Answer:

Show the answers and working

Density, pressure and exchange rates worksheet: Answers and working

1. 1200 people/km²
Population density = population ÷ area = 52800 ÷ 44 = 1200 people/km², that is 1200 people for each km² on average.
2. 7.9 g/cm³
Density = mass ÷ volume = 2370 ÷ 300 = 7.9 g/cm³: the unit g/cm³ is g ÷ cm³.
3. 41580, 50
Hong Kong dollars into yen multiplies: 2200 ÷ 100 × 1890 = 41580; yen into Hong Kong dollars divides: 945 ÷ 1890 × 100 = 50.
4. 14875 N/m²
Pressure = force ÷ area = 2975 ÷ 0.2 = 14875 N/m²: the smaller the area, the greater the pressure.
5. 9 kg
Mass = density × volume = 2.5 × 3600 = 9000 g; 1 kg = 1000 g, so 9000 g = 9 kg.
6. 42 minutes
Capacity = 120 × 40 × 70 = 336000 cm³ = 336 L (1 L = 1000 cm³); time = 336 ÷ 8 = 42 minutes.
7. 19300
1 m³ = 1000000 cm³ and 1 kg = 1000 g: 19.3 g/cm³ = 19.3 × 1000000 ÷ 1000 = 19300 kg/m³, that is, times 1000.
8. 1890, 450
3200 × 4.2 = 13440 New Taiwan dollars, 13440 − 11550 = 1890 left; back into Hong Kong dollars divides: 1890 ÷ 4.2 = 450.

9. C. 4171 Hong Kong dollars
Each pound buys 9.7 Hong Kong dollars, so 430 pounds buy 430 × 9.7 = 4171.
10. C. 1552 Hong Kong dollars
Each pound buys 9.7 Hong Kong dollars, so 160 pounds buy 160 × 9.7 = 1552.
11. False
1 m³ = 1000 L, so 1.2 m³ = 1200 L; time = volume ÷ flow rate = 1200 ÷ 15 = 80 minutes.
12. B. In Japan
The Japanese price comes to 8955 ÷ 1990 × 100 = 450 Hong Kong dollars against 510 in Hong Kong: in one currency, the lower price is the cheaper.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 372000 people
Population density = population ÷ area, so population = density × area = 60000 × 6.2 = 372000.
14. False
Pressure = force ÷ area, the force 27 N both times: 27 ÷ 200 and 27 ÷ 100. The smaller face gives the greater pressure.
15. 22500, 225
Capacity = 5 × 3 × 1.5 = 22.5 m³ = 22500 L (1 m³ = 1000 L); time = 22500 ÷ 100 = 225 minutes.
16. 44, 8
Volume = mass ÷ density = 849.2 ÷ 19.3 = 44 cm³; 52 − 44 = 8 cm³. The same mass in a bigger volume is less dense: a lighter metal is mixed in.
17. C. Shop B
A: 4400 ÷ 100 × 1900 = 83600 yen; B: (4400 − 50) ÷ 100 × 1980 = 86130 yen. A better rate doesn't always give more: count the fee too.
18. True
Pressure = force ÷ area, the force 53 N both times: 53 ÷ 50 and 53 ÷ 100. The smaller face gives the greater pressure.

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