Question

Find the area of a circle whose diameter is
(i) 8.4 cm
(ii) 5.6 m
(iii) 7 km

Answer 1

(i) Let r be the radius of the circle. Then, r = 8.4 $÷$ 2 = 4.2 cm.
∴ Area of the circle = ${\mathrm{\pi r}}^2$
$$\begin{gathered} \Rightarrow A=\frac{22}{7}\times {\left(4.2\right)}^2{\mathrm{cm}}^2 \\ \Rightarrow A=\left(\frac{22}{7}\times 4.2\times 4.2\right){\mathrm{cm}}^2=\left(22\times 0.6\times 4.2\right){\mathrm{cm}}^2=55.44{\mathrm{cm}}^2. \end{gathered}$$.

(ii) Let r be the radius of the circle. Then, r = 5.6 $÷$ 2 = 2.8 m.
Area of the circle = ${\mathrm{\pi r}}^2$
$$\begin{gathered} \Rightarrow A=\frac{22}{7}\times {\left(2.8\right)}^2{\mathrm{m}}^2 \\ \Rightarrow A=\left(\frac{22}{7}\times 2.8\times 2.8\right){\mathrm{m}}^2=\left(22\times 0.4\times 2.8\right){\mathrm{m}}^2=24.64{\mathrm{m}}^2. \end{gathered}$$​
(iii) ​​Let r be the radius of the circle. Then, r = 7 $÷$ 2 = 3.5 km.
Area of the circle = ${\mathrm{\pi r}}^2$
$$\begin{gathered} \Rightarrow A=\frac{22}{7}\times {\left(3.5\right)}^2{\mathrm{km}}^2 \\ \Rightarrow A=\left(\frac{22}{7}\times 3.5\times 3.5\right){\mathrm{km}}^2=\left(22\times 0.5\times 3.5\right){\mathrm{km}}^2=38.5{\mathrm{km}}^2. \end{gathered}$$