The radius of a quarter circle is 4 kilometers. What is the quarter circle's perimeter?

14.283 km

Step-by-step explanation:

The circumference of the entire circle is given by ...

C = 2πr

so the length of the curved perimeter of the quarter-circle is 1/4 of that:

1/4C = (1/4) 2πr = (π/2) r

The straight sides of the quarter-circle are both equal to the radius, so the total of all sides of the quarter-circle is ...

P = 2r + (π/2) r = (2+π/2) r

P ≈ (3.570796) (4 km) ≈ 14.283 km

The quarter-circle's perimeter is about 14.283 km.