Question

Find the area of the shaded region:

Answer 1

∵ Diameter of complete circle = 14 cm

∴ Radius = `14/2` = 7 cm  ...`[∵ "Radius" = "Diameter"/2]`

So, area of complete circle = πr² = `22/7 xx 7 xx 7` = 154 cm²

∵ Diameter of small circle = `7/4`cm

∴ Radius = `7/(4 xx 2) = 7/8`cm

∴ Area of two small circles = 2 × πr²

= `2 xx 22/7 xx 7/8 xx 7/8`

= `77/16`cm²

∴ Area of shaded region = Area of complete circle – Area of two small circles

= `154 - 77/16` 

= `(154 xx 16 - 77)/16`  ...[Taking LCM]

= `(2464 - 77)/16`

= `2387/16`

= `149 3/16`cm²

Hence, the area of shaded region is `149 3/16`cm².