How do you find the radius, diameter and circumference of a circle with an area of 64 cm2?

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Answer 1 · 2018-06-09T18:37:54

$A = 64 c m^{2}$ $A=64cm^2$

$r \approx 4.51 c m$ $r~~4.51cm$

$d \approx 9.03 c m$ $d~~9.03cm$

$C \approx 28.36 c m$ $C~~28.36cm$

First let's find the radius $r$ $r$ then we can solve the other questions:

Area formula:

$A_{circle} = π r^{2}$ $A_"circle" = pir^2$

$\frac{A}{π} = r^{2}$ $A/pi = r^2$

$\pm \sqrt{\frac{A}{π}} = \sqrt{r^{2}}$ $+-sqrt(A/pi) = sqrt(r^2)$

we can ignore the negative solution because a radius can't be negative in length:

$r = \sqrt{\frac{A}{π}} = \sqrt{\frac{64}{π}} \approx 4.51$ $r=sqrt(A/pi)=sqrt(64/pi)~~4.51$

Diameter formula:

$d = 2 r = 2 \sqrt{\frac{64}{π}} \approx 9.03$ $d=2r=2sqrt(64/pi)~~9.03$

Circumference formula:

$C_{circle} = 2 π r$ $C_"circle" = 2pir$

$C = 2 π \sqrt{\frac{64}{π}} \approx 28.36$ $C= 2pisqrt(64/pi)~~28.36$