If the area of a circle in square feet equals its radius in feet, then

Question

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

generis · Answer

Using this approximation:  \pi\approx{3.14}\approx{\frac{22}{7}}

Area of a circle = radius of a circle

A =\pi r^2= \pi * r*r 
 A=r 
 \pi*r*r=r 
Divide by  r 
 \pi*r=1 
We need the length of the radius: 
 r =\frac{1}{\pi}\approx{\frac{1}{3.14}}\approx{.32}

Answer B

Or find radius this way (whatever is easier): 
 r =\frac{1}{\pi}\approx{\frac{1}{\frac{22}{7}}}=(1*\frac{7}{22})\approx{.32}

Abhishek009 · Answer

r  =  πr^2

Or,  1 = \frac{22r}{7}

Or,  r = \frac{7}{22}

Or, r  ~  0.32 , Answer must be (B)

ScottTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

SOLUTION:

Given ∏R2 =R
=> R = 1/∏ =7/22
(Now we know 1/22 as a percentage is 4.16 and hence 7/22 will be 4.16*7 = 29.12%)
Closest option as a decimal is (b) as (a) is anyhow smaller than 29.12 and the rest of the options are very far from 29.12%)

OPTION B

Hope this helps

Devmitra Sen(Math)

BrushMyQuant · Answer

Area of Circle with radius r =  \pi r^2

Area of Circle = radius
=>  \pi r^2  = r
=>  \pi r^2  - r = 0
=> r ( \pi r - 1) = 0
=> r = 0 or  \frac{1}{ \pi} 
r cannot be 0 => r =  \frac{1}{ \pi}  = 1 /  \frac{22}{7} 
=> r =  \frac{7}{22}  ~  \frac{7}{21}  =  \frac{1}{3}  = 0.33

So,  Answer will be B 
Hope it helps!

Watch the following video to Learn Basics of Circles

https://www.youtube.com/watch?v=vDtyMOcDlCU

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