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An acre has a length of one furlong 1/8miand a width one-tenth of its length. (a) How many acres are in a square mile? (b) How many square feet are in an acre? See Appendix E. (c) An acre-foot is the volume of water that would cover 1 acre of flat land to a depth of 1 foot. How many gallons are in 1 acre-foot?

Short Answer

Expert verified

a) The area of an acre of land is 1640mi2. i.e., 640 acres to a square mile.

b) The number of square feet in an acre is 43,560ft2.

c) The gallons in 1 acre-foot are 3.25105gal.

Step by step solution

01

Concept of the length and Area

Length is a dimension of an object to describe how long the object is, and the area is length times width which defines the size of a closed region in a plane or two-dimensions.

02

Identification of given data

The given data can be listed below,

  • The length of an acre is,l=18mi.
  • The width of an acre is,w=110l=180mi.
  • The depth of an acre is,d=1ft.
03

(a) Determination of acres in a square mile

Area of an acre can be given as,

A=lw

Here, l is the acre鈥檚 length, and w is the width of the acre.

Substitute values in the above expression,

A=18mi180mi=1640mi2

Thus, an acre of the land area is1640mi2, i.e., 640 acres to a square mile.

04

(b) Determination of square feet in an acre

Conversion of a mile into the foot is given by,

1mi=5280ft

From the above conversion, the number of square ft in an acre is given by,

N=(1acre)1mi2640acre5280ft1mi2=43,560ft2

Thus, the number of square feet in an acre is 43,560ft2.

05

(c) Determination of gallons in 1 acre-foot

Gallon in one cubic foot can be given by,

1ft3=7.477gal

From the above conversion,

1acre-foot=43,560ft37.477gal1ft3=3.25105gal

Thus, the gallons in 1 acre-foot are 3.25105gal.

06

Final Solution

a) an acre of land comprises of1640th.part of a square mile.

b) an acre of land comprises of 43,560ft2

c) The number of gallons in 1 acre-foot are 3.25105gal.

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