In circle O, central angle AOB measures 72 degrees. The radius of the circle is r. The perimeter of sector AOB consists of line segments AO and BO and arc AB. Which expression gives the perimeter of sector AOB in terms of r?
(A) (π + 10) · r / 5
(B) (π + 8 ) · r / 4
(C) (π + 6) · r / 3
(D) (π + 2) · r / 5
(E) (2π + 10) · r / 5
(B) (π + 8 ) · r / 4
(C) (π + 6) · r / 3
(D) (π + 2) · r / 5
(E) (2π + 10) · r / 5
If the radius of the circle is r, then the circumference is 2πr. The angle AOB measures 72 degrees, which is 1/5 of the total degrees in a circle. Therefore, the measure of arc AB is 2πr/5. The perimeter of the whole section, then, would be 2πr/5, the length of the arc, plus 2r, the combined length of the two sides of the sector. (2πr/5) + 2r works out to be (2πr + 10r)/5, or (2π + 10) x r/5. The answer is (E).
source: crushthetest.com
