Question

Four circles are drawn side by side in a line and enclosed by a rectangle as shown below. If the radius of each of the circles is 3cm, then calculate: 1) the area of the rectangle. 2)the area of each circle. 3)the shaded area inside the rectangle.

Answer 1

Shaded Area is 30.96

Step-by-step explanation:

Let the four circles drawn be of the center, $O_1$,$O_2$,$O_3$ and $O_4$

Now, Let the rectangle that encloses the circles be ABCD

Length of the rectangle (AB) = Sum of Diameters of Circles

                                  = $4\times 6$

                                  = 24 cm

Breadth of Rectangle (BC) = Diameter of any circle

                                              = 6 cm

Area of Rectangle ABCD = $(Length)\times(Breadth)$

                                            = $24\times6$

                                            = $144 cm^2$

Area of circle with center O_1 = $\pi r^2$

                                                    = $\frac{22}{7}\times {3}\times{3}$

                                                    = $28.26 cm^2$

Area of 4 Circles = ${4}\times{28.26}$

                             = $113.04 cm^2$

Shaded Area = Area of rectangle ABCD - Area of 4 Circles

                       = 144 - 113.04

                       = $30.96 cm^2$

Shaded Area is $30.96 cm^2$