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Areas Related to Circles — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsAreas Related to Circles3 Marks
Question
A circular field has a perimeter of $650\ m.$ A square plot having its vertices on the circumference of the field is marked in the field. Calculate the area of the square plot.
✓

Answer

Perimeter of the circular field $= 650m$
$\therefore$ Radius $ (r) = \frac{\text{Circumference}}{2\pi} $
$=\frac{650\times7}{2\times22}=\frac{2275}{22}\text{m}$
$\therefore$ Diagonal of the inscribed square $=$ diameter of the circle
=$2\text{r}=2\times\frac{2275}{22}=\frac{2275}{11}\text{m}$
$\therefore\text{side}=\frac{\text{diagonal}}{\sqrt{2}}=\frac{2275}{\sqrt{2}\times11}$
and area of the squrae field $= a^2$
$=\Big(\frac{2275}{11\sqrt{2}}\Big)^2\text{m}^2=\frac{5175625}{121\times2}\text{m}^2$
$= 21386.88\text{m}^2$
$=21387\text{m}^2\text{(approx)}$

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