Question

Areas of some circles are given below find their diameters.
(1) 176 sq cm
(2) 394.24 sq cm
(3) 12474 sq cm

Answer 1

(1) 176 sq cm
$$\begin{gathered} \mathrm{Ar}=\mathrm{\pi }{r}^2 \\ \Rightarrow 176=\frac{22}{7}\times r^2 \\ \Rightarrow r^2=\frac{176\times 7}{22}=56 \\ \Rightarrow r=\sqrt{56} \\ d=2r=2\sqrt{56} \end{gathered}$$

(2) 394.24 sq cm
$$\begin{gathered} \mathrm{Ar}=\mathrm{\pi }{r}^2 \\ \Rightarrow 394.24=\frac{22}{7}\times r^2 \\ \Rightarrow r^2=\frac{394.24\times 7}{22}=125.44 \\ \Rightarrow r=11.2 \\ d=2r=2\times 11.2=22.4\mathrm{cm} \end{gathered}$$

(3) 12474 sq cm
$$\begin{gathered} \mathrm{Ar}=\mathrm{\pi }{r}^2 \\ \Rightarrow 12474=\frac{22}{7}\times r^2 \\ \Rightarrow r^2=\frac{12474\times 7}{22}=3969 \\ \Rightarrow r=63 \\ d=2r=2\times 63=126\mathrm{cm} \end{gathered}$$