radius and distance

Question

an oval track consists of 2 semicircles and a rectangle of length x, and width y. what is the radius of the semicircle ends? write an equation in terms of x

what is the radius of the semicircle ends? write an equation in terms of x and y for the distance around the oval

Answer 1

If we were to draw this oval track, the straight sides of the semicircles is joined at the width (shorter side) of the rectangle.

 

This means that the radius, r, is half the width.

 

r = y / 2

 

Then the distance around the oval is the sum of the two lengths of rectangle plus the circumference of full circle.  Note that 2 semicircles form a full circle.

 

Distance = 2x + 2πr

Distance = 2x + 2π(y/2)

Distance = 2x + πy