Question

. Assume you have a dot grid with 36 dots per sq.in. How many acres are represented by each dot using the following map scales: (a) 330 ft. per in., (b) 25 chains per in., (c) 1 mile per in.

Answer 1

To calculate the area represented by each dot on the dot grid, you need to consider the scale of the map. With a scale of 330 ft. per inch, 1 dot represents (330^2 / 43,560) acres. With a scale of 25 chains per inch, 1 dot represents ((25 chains)^2 / 10) acres. And with a scale of 1 mile per inch, 1 dot represents ((1 mile)^2 / 640) acres.

Step-by-step explanation:

The conversion from dots to acres varies depending on the scale:

1. (a) With a scale of 330 ft. per inch, we can calculate the area represented by each dot as follows:
   1 sq.in. = 330^2 sq.ft.
   1 acre = 43,560 sq.ft.
   Therefore, 1 dot represents (330^2 / 43,560) acres.
2. (b) With a scale of 25 chains per inch, we can calculate the area represented by each dot as follows:
   1 sq.in. = (25 chains)^2 sq.chains
   1 acre = 10 sq.chains
   Therefore, 1 dot represents ((25 chains)^2 / 10) acres.
3. (c) With a scale of 1 mile per inch, we can calculate the area represented by each dot as follows:
   1 sq.in. = (1 mile)^2 sq.miles
   1 acre = 640 acres
   Therefore, 1 dot represents ((1 mile)^2 / 640) acres.

Answer 2

a) 0.069 acres

b) 0.114acres

c) 17.78acres

Step-by-step explanation:

1 dot=1/36sqin

a) 1 sqin= 330×330=108900ft^2

1 dot=108900/36 =3025ft^2

Converting to acre,divide by43560

3025/43560 =0.069acre

b) 1 chain =22 yards

25×22=550yards

Converting to acre divide by 4840

550/4840 =0.114acre

c)1 sqmile =640acres

(1/36) ÷ 640

640/36

17.78acres