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Mensuration — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSMensuration1 Mark
MCQ
A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square?
  • A
    $\frac{3}{4}$ of original square.
  • ✓
    $\frac{1}{2}$ of original square.
  • C
    $\frac{1}{4}$ of original square.
  • D
    $\frac{2}{3}$ of original square.
✓

Answer

Correct option: B.
$\frac{1}{2}$ of original square.
Let a be the side of a square sheet.

Then, area of bigger square sheet $a^2...(i)$
Now, we make the circle of maximum possible size from it.
Then, the radius of circle $=\frac{\text{a}}{2} \ ...(\text{ii})$
So, its diameter $(d) =2\times\frac{\text{a}}{2}=\text{a}$
Now any square in a circle of maximum size will have the length of diagonal equal to the diameter of circle.
i.e. diagonal of square made inside the circle $= a$
So, the side of this square $=\frac{\text{a}}{\sqrt{2}} [\because$ diagonal $=$ side $\sqrt{2}]$
$\therefore$ Area of this square $=\frac{\text{a}^2}{2} \ ...(\text{iii})$
From Eqs. $(i)$ and $(iii),$
Area of this square is $\frac{1}{2}$ of original square.

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