Hi everybody, The figure here is a ring with a thickness shown in black. If the radius of the ring is r and the thickness of the ring is t, then which of the following expressions best describes the area of the ring? (A) π(r−t)2 (B) π(r2−t2) (C) 2π(r−2t) (D) πr(2r−t) (E) πt(2r−t) Could you please help me to undestand correct answer?

IMO E. The question is vague as it does not explicitly mention whether r is the internal radius or the external. Assuming that r is external radius. Radius of empty hole space = r-t Area of Ring will be Area of full circle - Area of empty hole Ï€ r^2 - Ï€ (r-t)^2 which simplifies to Ï€ t(2r-t) Hence E

EOV wrote:Hi everybody, The figure here is a ring with a thickness shown in black. If the radius of the ring is r and the thickness of the ring is t, then which of the following expressions best describes the area of the ring? (A) π(r−t)2 (B) π(r2−t2) (C) 2π(r−2t) (D) πr(2r−t) (E) πt(2r−t) Could you please help me to undestand correct answer? Consider the ring as two concentric circles. Since it is not given in question whether r is the radius of the outer circle or inner circle, Let's try both the cases... Case:1 The radius of inner circle is r The radius of outer circle is (r+t) Area of the Ring = Area of outer circle - Area of inner circle π(r+t)^2-πr^2 = πr^2 + πt^2 + 2πrt - πr^2 = πt^2 + 2πrt = πt(t+2r) Which is not in any of the options..... So r is the radius of Outer circle Case:2 The radius of outer circle is r The radius of inner circle is (r-t) Area of the Ring = Area of outer circle - Area of inner circle πr^2-π(r-t)^2 = πr^2 - πr^2 -πt^2 + 2πrt = 2πrt-πt^2 = πt(2r-t) Option E