Question

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?

Answer 1

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

Answer 2

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