Question

Determine the x component (in cm) of the centroid of the region below if a=14.6 cm, b=18.4cm and r=55cm. Do not round off in any intermediate steps. Express final answer in 5 SIGNIFICANT figures. No need to indicate the units.

y Fotot -b

Answer 1

given is :

a = 14.6 cm

b = 18.4 cm

r = 55 cm

- a a b

area of semicircle (A₁) = $\pi$ r²/2

= $\pi$ *55²/2

= 4751.658

area of triangle (A₂) = 1/2*(2a)*b

= 14.6*18.4

= 268.64

now, coordinate of centroid for semicircle disc is ( 4r / 3$\pi$ , 0)

distance of centroid from the origin in x - direction (X₁) = 4*55/3$\pi$

= 23.3427

thus distance of centroid of triangle from the origin in x - direction (X₂) = b/3 = 18.4/3

   = 6.1333

now, the centroid of composite area () = (A₁*X₁ - A₂*X₂)/(A₁ - A₂)

T

= (4751.658*23.3427 - 268.64*6.1333)/(4751.658 - 268.64)

= 24.373 cm