p.27
10. a.) How many cattle can 1 km2 support for a year?
We know 1 km2 produces 300 t of grain per year. This means it produces 300 000
kg of grain per year (1 t = 1000 kg)
We also know that a cow needs 7.7 kg of grain per day. This means it needs 7.7 kg x
365 days = 2810.5 kg of grain per year (since there are 365 days in a year)
So, we need to take the total amount of grain produced per year and see how many
times 2810.5 kg will go into it:
300 000 kg
2810.5 kg
= 106.74 cows
The 1 km2 can support ~107 cows.
b.) How many people can 1 km2 support for one year if the person ate only grain?
We know one person needs 2400 kJ/day. This means one person needs 2400
kJ/day x 365 days = 876 000 kJ/year
We need to find out how much energy the 1 km2 will produce by grain:
We know the 1 km2 contains 14 190/kg of grain. So how many kg of grain is in 1
km2? (we were given this in part a.)) 300 t = 300 000 kg/year
So, we take the amount of energy per kg and multiply by our total amount of kg:
14 190 kJ/kg x 300 000 kg/year = 4.257 x 109 kJ/year
Now, to find out the number of people this can support we take this total energy it
can produce and divide it by the amount of energy needed for one person per year:
4.257 x 109 kJ/year
876 000 kJ/year
= 4859.59 people
The field can support ~4860 people per year if they ate only grain.
c.) How many people can 1 km2 support for one year if the person ate only beef?
From part b.), we know that one person needs 876 000 kJ/year.
From part a.) we know that a 1 km2 field can support 106.74 cows per year.
We also know that beef contains 13 900 kJ/kg. And that one cow has a mass of 500
kg.
The total energy that the cows can produce can by found by finding their total mass
and multiplying it by the amount of energy per kg:
Total mass = 106.74 cows x 500 kg/cow = 53 370 kg of beef
Now, we need to find out how much energy is in beef for a year. So, take the total
amount of kg of beef and multiply the energy/kg:
53 370 kg x 13 900 kJ/kg = 7.418 x 108 kJ
To find out how many people this will support we take the total energy of the beef
and divide it by the amount of energy that one person needs per year:
7.418 x 108 kJ = 846.85 people/year
876 000 kJ
The field can support about 847 people per year if they eat only beef.
d.) Grain: 4859.59 people
Beef: 846.85 people
Therefore, grain is able to support more people.
******They don’t take into account that some land is more suitable for cattle then for
growing grain. As well, is there enough water to support a crop? Or enough people
to manage it? What about pesticide and fertilizer costs?******