Question

15. Three semicircles of radius 1 are constructed on diameter AB of a semicircle of radius 2. The centers of the small semicircles divide AB into four line segments of equal length. What is the area of the region that lies inside the large semicircle but outside the small semicircles?

Answer 1

Answer:

The remaining area = 4.201 m²

Explanation:

Given that

AB=D=  4 m  (R=2 m)

The area of AB semicircle

$A=\pi R^2/2$

A=2π

Thee area of small semicircle

a=5π/6 + 2√3/4  m²

a=5π/6 + √3/2  m²

So the remaining area = A-  a

                                     = 2π - (5π/6 + √3/2) m²

The remaining area =  2π - (5π/6 + √3/2) m²