Question

13. In the given figure; PQRS is a square inscribed in a circle
of diameter 14 cm. Calculate
(1) the area of the circle
(in the area of the shaded portion (Take π=22/7)​

Answer 1

Answer:

GIVEN:

• Diameter of circle = 14 cm. Thus, radius = ½Diameter = ½×14 = 7 cm.

• PQRS is a square. Thus, PQ=QR=RS=SP.

RTF:

(1) the area of the circle

(2) the area of the shaded portion (Take $\pi$ =22/7)​

SOLUTION:

Area of circle:

$A=\pi r^{2}$

Substitute the values:

$A=\frac{22}{7} \times 14^{2}$

$A=616\:cm^{2}$

Now, we know that PQRS is inscribed in the circle. ∴ The cirle and the square have a common centre.

We know that the diagonal PR is equal to the diameter of the circle.

Thus, PR=14 cm.

Now, we know that:

$diagonal \: of \: square \: = \sqrt{2} \times side$

$14=\sqrt{2} \times side$

$side = \frac{14}{\sqrt{2} }$

Rationalise $\frac{14}{\sqrt{2}}$. You will get:

$side = 7\sqrt{2} \: cm.$

Now, we know that area of square = side²

$\to (7\sqrt{2})^{2}$

$\to 98 \: cm^{2}$

Now, To find the area of the shaded region:

Area of shaded region = area of circle - area of square.

Area = 616-98

=518 cm²

HOPE THIS HELPS :D