Question

33

Ebony is making a scale drawing of her farm. The farm has a circular well with a circumference
of 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 ft
B 1 cm = 2.5 ft
C 1 cm = 5 ft
D 1 cm = 6.25 ft​

Answer 1

B

Explanation:

Circumference of a circle is:

C = 2πr

Area of a circle is:

A = πr²

The 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 = 2πR

0.641 = πr²

Solving for each:

R = 47 / (2π) ≈ 7.48 feet

r = √(0.641 / π) ≈ 0.452 cm

The scale is the ratio of R / r:

R / r = (7.48 ft) / (0.452 cm) = 16.6 ft/cm

So 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 feet

r = √(0.64π / π) = 0.8 cm

R / r = (2 feet) / (0.8 cm) = 2.5 ft/cm

So 1 cm = 2.5 ft.