Photo AI
Festival A will be in a rectangular field with an area of 80000 m² The greatest number of people allowed to attend Festival A is 425 - Edexcel - GCSE Maths - Question 5 - 2022 - Paper 2
Question 5
Festival A will be in a rectangular field with an area of 80000 m² The greatest number of people allowed to attend Festival A is 425. Festival B will be in a rectan... show full transcript
Worked Solution & Example Answer:Festival A will be in a rectangular field with an area of 80000 m² The greatest number of people allowed to attend Festival A is 425 - Edexcel - GCSE Maths - Question 5 - 2022 - Paper 2
Step 1
How much greater?
Answer
To find the area per person at each festival:
-
Festival A
- Area = 80000 m²
- Maximum attendees = 425
- Area per person = ( \frac{80000}{425} \approx 188.24 ) m²
-
Festival B
- Area = 700 m × 2000 m = 1400000 m²
- Maximum attendees = 6750
- Area per person = ( \frac{1400000}{6750} \approx 207.41 ) m²
-
Difference
- Difference = Area per person for Festival B - Area per person for Festival A = ( 207.41 - 188.24 \approx 19.17 ) m²
Therefore, the area per person for Festival B is approximately 19 m² greater than for Festival A (rounded to the nearest whole number).
Step 2
Explain why Callum's method is wrong.
Answer
Callum's method is incorrect because he misunderstood the conversion between cubic centimeters and cubic meters.
-
Conversion Factors: There are 100 cm in 1 m, which means there are 100 x 100 x 100 = 1000000 cm³ in 1 m³, not 100.
-
Correct Calculation: To convert 300 cm³ to m³, it should be:
- ( 300 , \text{cm}^3 \times \frac{1 , ext{m}^3}{1000000 , ext{cm}^3} = 0.0003 , ext{m}^3 )
Thus, Callum's conclusion of 3 m³ is incorrect as he did not properly account for the cube of the conversion factor.