If the area of a circle in square feet equals its radius in feet, then the circle's radius, in feet, is closest to

[M7MBA]

If the area of a circle in square feet equals its radius in feet, then the circle's radius, in feet, is closest to

A) 0.25
B) 0.32
C) 0.45
D) 0.5
E) 0.65

Answer: B

Source: Economist

[swerve]

If the area of a circle in square feet equals its radius in feet, then the circle's radius, in feet, is closest to

A) 0.25
B) 0.32
C) 0.45
D) 0.5
E) 0.65

Answer: B

Source: Economist

We have that,

\(r=\pi r^2\)

and using the approximation

\(\pi \approx 3.14 \approx \dfrac{22}{7}\)

Therefore,

\(1=\dfrac{22}{7}r \Longrightarrow r=\dfrac{7}{22}\approx 0.32\)

[Scott@TargetTestPrep]

If the area of a circle in square feet equals its radius in feet, then the circle's radius, in feet, is closest to

A) 0.25
B) 0.32
C) 0.45
D) 0.5
E) 0.65

Answer: B
Solution:

Let’s let r = the radius of the circle, in feet, and we can create the equation:

πr^2 = r

Dividing both sides by r (since r can’t be 0), we have:

πr = 1

r = 1/π ≈ 0.32

Answer: B