As a contrast between the old and the modern and between the large and the small, consider the following: In old rural England 1 hide (110 acres) was the area of land needed to sustain one family with a single plough for one year. (An area of 1 acre is equal to 4047 m2.) Also, 1 wapentake was the area of land needed by 100 such families. In quantum physics, the cross-sectional area of a nucleus (defined in terms of the chance of a particle hitting and being absorbed by it) is measured in units of barns, where 1 barn is 1 × 10-28 m2 (exactly). (In nuclear physics jargon, if a nucleus is “large,” then shooting a particle at it is like shooting a bullet at a barn door, which can hardly be missed.) What is the ratio of 22 wapentakes to 16 barns?

Question

As a contrast between the old and the modern and between the large and the small, consider the following: In old rural England 1 hide (110 acres) was the area of land needed to sustain one family with a single plough for one year. (An area of 1 acre is equal to 4047 m2.) Also, 1 wapentake was the area of land needed by 100 such families. In quantum physics, the cross-sectional area of a nucleus (defined in terms of the chance of a particle hitting and being absorbed by it) is measured in units of barns, where 1 barn is 1 × 10-28 m2 (exactly). (In nuclear physics jargon, if a nucleus is “large,” then shooting a particle at it is like shooting a bullet at a barn door, which can hardly be missed.) What is the ratio of 22 wapentakes to 16 barns?

Answer 1

To summarise: There are

100 hide per wapentake
110 acre per hide
4047 m^2 per acre
1E-28 m^2 per barn

Use these figures to convert 22 wapentake to barn. Divide that by 16 barn.

Answer 2

To find the ratio of 22 wapentakes to 16 barns, we need to calculate the area represented by each unit and then compare the two.

First, let's determine the area represented by 22 wapentakes. We are given that 1 wapentake is the area of land needed by 100 families, so 22 wapentakes would represent 22 * 100 = 2200 families. Since 1 hide (110 acres) was needed to sustain one family, the area represented by 22 wapentakes would be 2200 * 110 = 242,000 acres.

Next, we'll calculate the area represented by 16 barns. We know that 1 barn is equal to 1 × 10^(-28) m^2, so 16 barns would be 16 * (1 × 10^(-28)) = 1.6 × 10^(-27) m^2.

Now, we need to convert the area in acres to square meters. Given that 1 acre is equal to 4047 m^2, the area represented by 22 wapentakes would be 242,000 * 4047 = 979,734,000 m^2.

Finally, we can calculate the ratio of 22 wapentakes to 16 barns by dividing the area represented by wapentakes by the area represented by barns: 979,734,000 m^2 / (1.6 × 10^(-27) m^2).

To simplify the calculation, we can convert the area in scientific notation. The denominator becomes 1.6 × 10^(-27) m^2 = 16 × 10^(-28) m^2.

Dividing the numerator by 16 and subtracting 1 from the exponent:

= (979,734,000 m^2) / (16 × 10^(-28) m^2)
= (61,233,375) / (10^(-28))
= (6.1233375) × (10^29)
≈ 6.123 × (10^29)

Therefore, the ratio of 22 wapentakes to 16 barns is approximately 6.123 × (10^29).