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Natty97
25 pi = pi *r^2

r = 5

2*pi*r (circumference of can) = 10*pi

water ring that is 10% larger = 1.1(10*pi)
= 11*pi<<-------------This is the measure of circumference of water ring. We are asked to determine the area of water ring.

Answer is E

Hi Natty97,
Please refer the highlighted portion above, circumference of water ring=\(11\pi\)
Or, \(2\pi\)*radius of circular water ring=\(11\pi\)
Or, Radius of water ring=\(\frac{11}{2}\)

So, Area of water ring=\(\pi*(\frac{11}{2})^2=30.25\pi\)

Ans. (D)
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Bunuel
A cylindrical can placed on a table leaves a water ring that is 10% larger than the circumference of the bottom of the can. If the area of the bottom of the can is 25π, which of the following is area encircled by the water ring?


A. \(121\pi\)
B. \(110\pi\)
C. \(55\pi\)
D. \(30.25\pi\)
E. \(11\pi\)


Circumference is 2πr..
So if we increase circumference by 10%, the effect will be on the radius only as other term 2π is constant...
So r becomes 1.1r

Now initial area =\(\pi*r^2=25\pi\)
And the new area is \(π*(1.1r)^2=π*1.21*r^2=1.21*πr^2=1.21*25=30.25\)

D
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Natty97
25 pi = pi *r^2

r = 5

2*pi*r (circumference of can) = 10*pi

water ring that is 10% larger = 1.1(10*pi)
= 11*pi

2*pi*R = 11*pi
R= 11/2

The area is pi∗(11/2)^2 = 30.25*pi

Answer is D

Thanks PKN

You are welcome.
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Bunuel
A cylindrical can placed on a table leaves a water ring that is 10% larger than the circumference of the bottom of the can. If the area of the bottom of the can is 25π, which of the following is area encircled by the water ring?


A. \(121\pi\)
B. \(110\pi\)
C. \(55\pi\)
D. \(30.25\pi\)
E. \(11\pi\)


pi * r2 = 25 pi
r= 5

1.1* 5 = 5.5
5.5^2 * pi = 30.25 pi
IMO D
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