geometry question

[blueland78]

THin conveyor belt 15ft long is drawn tightly around two circular wheels each 1ft in diameter. what is the distance between the centers of the two wheels?

a)15-pi/2
b)5pi/4
c)15-2pi
d)15-pi
e)2pi

the drawing looks like engine belt , if that helps.
would you please explain how to get a as an answer in detail plz?

[malolakrupa]

The answer is 15 - 2pi which is c.the distance between the 2 centers is

15 - (2* (2* pi*1)/2) Hence c

[sibbineni]

The conveyor belt only goes around half of the wheel.

For wheel1 it covers half the circumference =1/2 * pi.

For wheel 2 it covers half the circumference = 1/2 * pi.

for 2 wheels it covers=pi

so we have 15-pi which is the length of the belt that goes top and bottom
but not around 2 wheels

here we have to find the distance between centres of 2 wheels

so we have to divide 15-pi by 2 to get the length between the centers of the 2 wheels.


IMO A

[malolakrupa]

My bad , it is A .