Question

In the given fig, the cross type figure is divided into five squares.The side of each square is 2 cm, then find the radius of the circle and also the area of portion between circle and cross type figure(Take $\pi$ 3.14).

• A. $\sqrt{10}$ cm, 11.40 $c{m}^2$
• B. $\sqrt{11}$ cm, 12.40 $c{m}^2$
• C. $\sqrt{12}$ cm, 10.40 $c{m}^2$
• D. None of these

Answer 1

The correct option is A $\sqrt{10}$ cm, 11.40 $c{m}^2$

If a circle passes through $4$ vertices of rectangle then the diagonal is equal to the diameter of the circle.
In $△ABC$,
$\angle B=90$
$BC=(2+2+2)$
$=6cm$
$AB=2cm$
$A{C}^2=A{B}^2+B{C}^2$
$=>A{C}^2=2^2+6^2$
$=4+36$
$=40$
$=2\sqrt{10}$
AC=diameter of the circle
Therefore,
Radius$=\frac{2\sqrt{10}}{2}$
$=\sqrt{10}cm$
Area of a circle=$\pi r^2$
$=3.14\times (\sqrt{10}{)}^2$
$=3.14\times 10$
$=31.4c{m}^2$
Area of cross type figure=Area of $5$ squares
$=5\times 2\times 2$
$=20sqcm$
Area of portion between circle and cross type figure=Area of circle-Area of cross type figure
$=3.14-20$
$=11.4c{m}^2$
Therefore,
Radius of circle$=\sqrt{10}cm$
Area of portion between circle and cross type figure
$=11.4c{m}^2$