Question

1. although the preferred si unit of area is a m², land is often measured in hectares (ha). one hectare is equal to 10,000 m². therefore, 1 ha = ______ km² if the density of silver maples in a 5x5 mile section of forest is 7 trees/mi², what is its density per hectare? (5280 feet = 1 mile)

Explanation:

Step1: Convert 1 hectare to square - kilometers

We know that 1 ha = 10000 m², and 1 km = 1000 m, so 1 km²=(1000 m)×(1000 m)=1000000 m². Let \(x\) be the area in km² of 1 hectare. Then \(x=\frac{10000}{1000000}=0.01\) km².

Step2: Convert square - miles to hectares

First, find the area of the forest section in square - miles. The area \(A = 5\times5=25\) mi².
We know that 1 mile = 5280 feet and 1 foot = 0.3048 m. So 1 mile \(=5280\times0.3048 = 1609.344\) m. Then 1 mi²=(1609.344 m)×(1609.344 m)\(\approx2.59\times10^{6}\) m². And 1 ha = 10000 m², so 1 mi²=\(\frac{2.59\times 10^{6}}{10000}=259\) ha.
The number of trees in the 25 - mi² forest is \(N = 7\times25 = 175\) trees.
The area of the forest in hectares is \(A_{ha}=25\times259 = 6475\) ha.
The density of trees per hectare \(d=\frac{175}{6475}\approx0.027\) trees/ha

Answer:

1 ha = 0.01 km²; The density of silver - maples per hectare is approximately 0.027 trees/ha