The circumference of a circular field is 396 m and that of the other circular field is 132 m. Find the area (in m2) of the third circular field whose radius is the sum of the radii of the first two fields. (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 22176
Each radius comes from its circumference, \(C=2\pi r\), so \(\displaystyle r=\frac{C}{2\pi}\). The third field’s area is then \(\pi R^2\) with \(R\) the sum of the two radii.
First field: \(\displaystyle r_1=\frac{396\times7}{2\times22}=63\) m
Second field: \(\displaystyle r_2=\frac{132\times7}{2\times22}=21\) m
Third field: \(R=63+21=84\) m
Area \(\displaystyle =\frac{22}{7}\times84\times84=22\times12\times84=22176\,\mathrm{m^2}\)
Shortcut: Radius is proportional to circumference, so the radii can be added through the circumferences.
Circumference of the third field \(=396+132=528\) m
\(\displaystyle R=\frac{528\times7}{44}=84\) m, the same radius in one step