Question

If the $4$ equal circles of radius $3cm$ touch each other externally then the area of the region bounded by $4$ circles is ___ .

• A. $4(9-\pi )c{m}^2$
• B. $9(4-\pi )c{m}^2$
• C. $5(6-\pi )c{m}^2$
• D. $6(5-\pi )c{m}^2$

Answer 1

The correct option is B $9(4-\pi )c{m}^2$

Area of shaded region

$=$ Area of square - 4$\times$ area of 1 quadr

$=$ ${\left(AB\right)}^2-4\times \frac{1}{4}\times \pi r^2$

$=$ ${\left(6\right)}^2-\pi \times 3\times 3$

$=$ $36-9\pi =9(4-\pi ){cm}^2$