Chunk of Pi.

Geometry Level 2

The radius of a circle is equal to its area numerically. What is the circumference of this circle?

2 π 2 \pi 2 1 π \pi

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16 solutions

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Pedro Ramirez
Dec 21, 2013

The area A A of a circle is given by A = π r 2 A = \pi r^2 , where r r is the radius of the circle.

Since A = r A = r by hyphotesis, we have r = π r 2 r = \pi r^2 , which means 1 = π r 1 = \pi r .

Since the circumference L L of a circle is given by L = π ( 2 r ) L = \pi (2 r) and 1 = π r 1 = \pi r , then L = 2 ( 1 ) = 1 L = 2(1) = 1 .

L=2(1)=2

shaheed vh - 7 years, 5 months ago

True, I missed that.

Pedro Ramirez - 7 years, 5 months ago

how?

Faisal Tahir - 7 years, 5 months ago
Hanissa S
Dec 21, 2013

We are given r = π r 2 r=\pi r^{2} Dividing both sides by r r , we get π r = 1 \pi r= 1 then r = 1 π r=\frac{1}{\pi} The formula for a circle's circumference is 2 π r 2\pi r . Hence, the circumference is 2 × π × 1 π = 2 2\times\pi\times\frac{1}{\pi}=2

I did the same way

Pamandeep Singh Puri - 7 years, 2 months ago

The radius of a circle is equal to its area.

  • R = π \pi R ²
  • 1 = π \pi R

The circumference of a circle is 2 π \pi R , then:

  • 2 π \pi R = 2 × 1 2 \times 1

Thus, the circle's circumference is 2 units.

Amogh Joshi
Dec 21, 2013

pi x r x r = r, therefore. pi x r=1 therefore 2 x pi x r = 2

Carl Denton
Dec 21, 2013

From the problem we know that π r 2 = r \pi r^2 = r , so π r = 1 \pi r = 1 , and r = 1 π r = \frac{1}{\pi} . Plugging this in for circumference, we have 2 π r = 2 π 1 π = 2 2\pi r= 2\pi\frac{1}{\pi} = 2 .

Henry Okafor
Jan 17, 2014

Since area = radius

Therefore, p i × r r pi \times r * r = r

Hence, p i × r pi \times r = 1

But, circumference of a circle is 2 * p i × r pi \times r = 2 × 1 2 \times 1 = 2

Shashank Tiwari
Dec 21, 2013

We Have πr²=r.....→ Dividing Throughout By ’r’ We Get πr=1.....eqn 1.....Now To Get Circumference i.e 2πr Simply multiply eqn 1 By 2 We Get 2πr=2.Thus Circumference =2

Shubham Shah
Mar 26, 2014

Let the radius be r. Let the area of circle = PI* r r. Now solving both we will get only PI r. -------------------------(1) Circumference of circle =2 PI r.-----------------------------------(2) Solving (1) &(2). We will only get 2.

Hema Radha
Feb 4, 2014

area of circle = pi r^2. circumference of circle=2 pi r here r=pi r^2 r=1/pi circumference =2

The area of a circle is equal to π r 2 \pi r^2 .

Since the area is numerically equal to the radius, we let r r be the area. Therefore,

r = π r 2 r = \pi r^2

r r 2 = π \frac{r}{r^2} = \pi

1 r = π \frac{1}{r} = \pi

r = 1 π r = \frac{1}{\pi}

We now have the value for r r . Let's put it to the formula for the circumference of the circle, which is C = 2 π r C = 2 \pi r , since we are dealing with the radius.

C = 2 π r C = 2 \pi r

C = 2 π ( 1 π ) C = 2 \pi (\frac{1}{\pi})

C = 2 C = \boxed{2}

There. The circumference of the said circle is 2 2 units.

Mardokay Mosazghi
Jan 19, 2014

since the area and the circumference are numerically equal πr^2=2πr then you solve the equation' then you get 2 as the answer.

In a sense you could also get -2 as the answer.

let the radius = r area=πr² area=r r=πr² divided by r 1=πr r=1/π circumference =2πr but r=1/π =2π/π=2

Queen Ang3l
Dec 30, 2013

r=pi r^2

1/pi=r

C=1/pi x 2 x pi

C=2

Arjun S Xetry
Dec 22, 2013

Its very simple. Here r = π r 2 π r = 1 r=\pi r^2\Rightarrow\pi r=1 . Hence 2 π r = 2 2\pi r=2 which is the required circumference.

Budi Utomo
Dec 22, 2013

We know from that clue that r = phi x r^2 "areas" ---> So, 1 = phi x r ---> r = 1/ phi. Then, the solution is the circumference of circle is 2 x phi x r = 2 x phi x 1/phi = 2. Answer : 2

Raymond Julianto
Dec 21, 2013

22/7 * x * x= x
x (radius)=7/22
Diameter=7/22 * 2= 7/11
Circumference=22/7 * 7/11=2


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