All about circles

Geometry Level 1

The circle has a circumference that is numerically equal to its area.

What is the diameter of this circle?

2 4 6 8 10

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3 solutions

Toshit Jain
Mar 13, 2017

G i v e n , 2 π r = π r 2 Given \space , \space 2\pi{r} \space =\space \pi r^{2}

r = 2 \Rightarrow \space r \space =\space 2

2 r = 4 \boxed{\therefore \space 2r \space= \space 4 }

Matthew Warwick
May 9, 2017

Area = π \pi r 2 ^{ 2 }

Circumference = π \pi d

If they are equal, π \pi r 2 ^{ 2 } must equal π \pi d

This simplifies to r 2 ^{ 2 } = d

d=2r, so squaring must equal multiplying by 2.

This gives the radius as 2.

Continuing this, we get 2r = d.

r = 2, so 2 × \times 2 = d

d = 4.

Francisc Visky
May 9, 2017

πD²/4=πD → D/4=1→ D=4

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