Question

a body is moving in circle of radius R . the body move through half circle. calculate distance and displacement

Answer 1

Distance and displacement will be same.

That will be half the circumference!

C=2piR/2

i.e, piR

Answer 2

given,

the body is moving in a circle of radius r

theory ,
displacement is the shortest distance travelled by the object .
distance is the total path taken by the object


according to your theory in this case,

distance =
$2\pi \times r \div 2$
(we take circumference of circle because we need the path length not the area
as it is in travelled by half circle be divided by 2)

displacement =2r or the diameter
(as diameter is the shortest distance travelled,2r are would be the displacement)

hope it helps