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Wind turbines are used as an alternative way to generate electricity - NSC Mathematical Literacy - Question 3 - 2024 - Paper 2
Question 3
Wind turbines are used as an alternative way to generate electricity. The picture below shows how the size of the wind turbine and the generation capacity has change... show full transcript
Worked Solution & Example Answer:Wind turbines are used as an alternative way to generate electricity - NSC Mathematical Literacy - Question 3 - 2024 - Paper 2
Step 1
Step 2
3.1.2 Give ONE possible reason why the rotor blade size of the wind turbine from 2005 is larger than the rotor blade size of the wind turbine from 1980.
Answer
One possible reason for the larger rotor blade size in the 2005 wind turbine is the increased demand for electricity, which necessitates larger turbines that can capture more wind energy, thereby producing more electricity.
Step 3
3.1.3 Calculate, in metres, the maximum height that the tip of the rotor blade of the tallest wind turbine can reach as it turns.
Answer
The maximum height is calculated by adding the hub height to the rotor radius. Given that the rotor diameter is 124 m, the radius is 62 m. Thus:
Maximum height = Hub height + Rotor radius
Maximum height = 114 m + 62 m = 176 m.
Step 4
3.1.4 Anam says that the area covered by the rotor blade of the tallest wind turbine can be calculated as 12 077,848 m². Verify, with calculations, whether or not her statement is VALID.
Answer
To verify Anam's statement, we calculate the area of the circle using the formula for the area:
Using the radius of 62 m:
Anam's statement is VALID.
Step 5
3.1.5 Determine the percentage increase in power generation from 1995 to 2005.
Answer
The power generation in 1995 was 800 kW, and in 2005 it was 5 000 kW. The percentage increase can be calculated as follows:
Percentage increase = ( \frac{5 000 - 800}{800} \times 100% = \frac{4 200}{800} \times 100% = 525% )
Step 6