MATH SOLVE

3 months ago

Q:
# 33Ebony is making a scale drawing of her farm. The farm has a circular well with a circumferenceof 47 feet. In the drawing, the area of the well will be 0.641 square centimeters.What scale is Ebony using?A 1 cm = 0.16 ftB 1 cm = 2.5 ftC 1 cm = 5 ftD 1 cm = 6.25 ft

Accepted Solution

A:

Answer:BStep-by-step explanation:Circumference of a circle is:C = 2πrArea of a circle is:A = πr²The circumference of the well is 47 ft and the area of the well in the drawing is 0.641 cm². If we say r is the radius of the circle on the drawing in centimeters and R is the actual radius of the well in feet, then:47 = 2πR0.641 = πr²Solving for each:R = 47 / (2π) ≈ 7.48 feetr = √(0.641 / π) ≈ 0.452 cmThe scale is the ratio of R / r:R / r = (7.48 ft) / (0.452 cm) = 16.6 ft/cmSo 1 cm = 16.6 ft.This isn't one of the options. Are you sure you copied the problem correctly?Maybe you meant that the circumference is 4π feet, and the area is 0.64π cm². If so:R = 4π / (2π) = 2 feetr = √(0.64π / π) = 0.8 cmR / r = (2 feet) / (0.8 cm) = 2.5 ft/cmSo 1 cm = 2.5 ft.