Multistep A museum groundskeeper is creating a semicircular statuary garden with a diameter of 30 feet. There will be a fence around the arden. The fencing costs per linear foot. About how much will the $9.25 fencing cost altogether?

Recognize that the fencing will encompass an areathat is made up of a curved arc that is half of acircle plus a straight portion that is the diameter. We will be adding the arc length plus the diameterto get the total perimeter of the garden. d=30 feet ... diameter of circleθ=180º ... central angle of a semicircleA = (θº/360º) πd ... arc length of a sectorP ... total perimeter So let's write our equation for total perimeter ... P=A+d ... total perimeter equals arc length plus diameter = (θº/360º) πd + 30 = (180/360) (3.14) (30) + 30 ... substitute for variables = (1/2) (3.14) (30) + 30 ... simplify = 47.12 + 30∴ P=77.12 feet Now let's calculate the total fencing cost ... $TOT=P x ($cost per foot) = 77.12 x $9.25∴ $TOT=$713.40

Semicircle perimiter=1/2circumferece+diameteter

diameter=2r

c=2pir

so 1/2circumference=1/2 (2pir) = pir

d/2=r

given

d=30

d/2=30/2=15=r

perimiter=pir+d

perimiter=15pi+30

aprox

perimiter=77.1239

total cost=cost per foot times feet

total cost=9.25 times 77.1239

total cost=713.396

it will cost $713.40