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?
Circular Ring With Thickness
This topic has expert replies
- eaakbari
- Master | Next Rank: 500 Posts
- Posts: 435
- Joined: Mon Mar 15, 2010 6:15 am
- Thanked: 32 times
- Followed by:1 members
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
π r^2 - π (r-t)^2
which simplifies to
Ï€ t(2r-t)
Hence 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
π r^2 - π (r-t)^2
which simplifies to
Ï€ t(2r-t)
Hence E
Whether you think you can or can't, you're right.
- Henry Ford
- Henry Ford
- nisagl750
- Master | Next Rank: 500 Posts
- Posts: 145
- Joined: Tue Jan 31, 2012 6:50 am
- Location: New Delhi
- Thanked: 16 times
- Followed by:2 members
- GMAT Score:760
Consider the ring as two concentric circles.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?
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
Ï€(r+t)^2-Ï€r^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
Ï€r^2-Ï€(r-t)^2
= πr^2 - πr^2 -πt^2 + 2πrt
= 2Ï€rt-Ï€t^2
= πt(2r-t)
Option E