Question

Find the area of the shaded region. Express your answer in terms of pi

Answer 1

Area of the shaded region is 540 – 65.25π.    

Solution:

Length of the rectangle = 12 + 9 + 6 + 3 = 30 in

Width of the rectangle = 18 in

Radius of the larger circle ($r_1$) = 12 ÷ 2 = 6 in

Radius of the medium circle ($r_2$) = 9 ÷ 2 = 4.5 in

Radius of the smaller circle ($r_3$) = 6 ÷ 2 = 3 in

Area of the shaded region = Area of the rectangle – Area of the larger circle – Area of the medium circle – Area of the smaller circle

                                   $=l\times b-\pi r_1^2-\pi r_2^2-\pi r_3^2$

                                   $=30\times 18-\pi \times 6^2-\pi \times (4.5)^2-\pi \times 3^2$

                                   $=540-36\pi-20.25\pi-9\pi$

                                   $=540-65.25\pi$

Area of the shaded region is 540 – 65.25π.