What is the area of a circle with a circumference of 56.52 inches (in.)? Use 3.14 forimage.

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Answer 1 · 2018-06-05T17:11:18

$\approx 254 {in}^{2}$ $~~254 "in"^2$

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

$56.52 = 2 π r$ $56.52= 2pir$

$28.26 = π r$ $28.26=pir$

$r = \frac{28.26}{π} \approx 8.995$ $r=28.26/pi~~8.995$

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

$A_{circle} = π {(8.995)}^{2} \approx 254.19$ $A_"circle" = pi(8.995)^2~~254.19$

We can combine the formulas:

$C = 2 π r$ $C = 2pir$

$\frac{C}{2 π} = r$ $C/(2pi) = r$

$A = π {(\frac{C}{2 π})}^{2}$ $A = pi(C/(2pi))^2$

$A = π \frac{C^{2}}{4 π^{2}}$ $A = piC^2/(4pi^2)$

Now we have a formula for the area of a circle of any given circumference:

$A = \frac{C^{2}}{4 π}$ $A = C^2/(4pi)$

$C = 56.52$ $C=56.52$

$A = \frac{{56.52}^{2}}{4 π} \approx 254.19$ $A = 56.52^2/(4pi) ~~254.19$

Answer 2 · 2018-06-05T19:42:22

$254.34 {in}^{2}$ $254.34 "in"^2$

$:."circumference of a circle"=2pir$

$:.2pir=56.52"in"$

$:.r=56.52/(2pi)$

$:.r=56052/(2 xx3.14)$

$:.r=56.52/6.28$

$:.r=9$

$:."Area of a circle"= pi r^2$

$:.A=3.14 xx9^2$

$:.A=254.34"in"^2$