Q) Find the area of the unshaded region shown in the given figure.

Find the area of the unshaded region shown in the given figure. CBSE 10th board Sample paper 2023 Important questions

Ans:

Let’s redraw the diagram:

Find the area of the unshaded region shown in the given figure. CBSE 10th board Sample paper 2023 Important questions

As we can see in the diagram, in the center area:

diameter of semicircle (2R) = side of the inside square (S)

or S = 2R ………………. (i)

Also we see that Side of larger square = Gap from left side + radius of left semicircle + side of inside square + radius of right semicircle + gap from right side

14 = 3 + R + S + R + 3

2R + S = 8

\therefore R = 2 cm     (S = 2R from equation (i)

and side of the square, S  = 2R = 4 cm

We can see that the area of center region = 4 x area of semicircle + area of inside square

= 4 \pi (\frac{r^2}{2}) + (S)2

= 4 \pi (\frac{(2)^2}{2}) + (4)= 8 \pi + 16

= 8 $(\frac{22}{7}) + 16 = 41.14 cm2

Therefore, the area of unshaded region in the center is 41.14 cm2.

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top