Class X Session 2023-24 Question 26

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041)

Question 26

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

Solution:

modified view of shared image

The total horizontal or vertical extent of the region is 8 cm and extent includes the side length of the square (𝑎) 

and the diameters of the semicircles on either side of the square.

Given that each semicircle has a radius 𝑟, the side length of the square is 𝑎=8−2𝑟.

Given the figure, the radius 𝑟 of each semicircle is 2cm

Side Length of the Square 𝑎 = 8-2x2  = 4 cm

Area of the Square:  𝑎^2 = 4^2 = 16

Area of One Semicircle = \[ \frac{1}{2} {\pi} r^2 = 2{\pi} \; cm^2\; where \; r= 2 \]

Combined Area of Four Semicircles: \[4\times 2\pi\; cm^2\]

Area of the unshaded region=Area of the square + 4 x Area of  one semicircle =

\[16 \; cm^2 + 4 \times2 {\pi} \; cm^2 \]

\[(\;16 + 8{\pi}\;) \; cm^2\]