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A circular pool of radius r feet is surrounded by a circular sidewalk
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18 Feb 2021, 00:25
18 Feb 2021, 00:25
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A circular pool of radius r feet is surrounded by a circular sidewalk of width \(\frac{r}{2}\) feet. In terms of r, what is the area of the sidewalk?
A. \(2 \pi r^2\)
B. \(\frac{5 \pi r^2}{4}\)
C. \(\frac{9 \pi r^2}{4}\)
D. \(\pi r^2\)
E. \(\frac{\pi r^2}{2}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(2 \pi r^2\)
B. \(\frac{5 \pi r^2}{4}\)
C. \(\frac{9 \pi r^2}{4}\)
D. \(\pi r^2\)
E. \(\frac{\pi r^2}{2}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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A circular pool of radius r feet is surrounded by a circular sidewalk
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18 Feb 2021, 01:06
18 Feb 2021, 01:06
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Carcass wrote:
A circular pool of radius r feet is surrounded by a circular sidewalk of width \(\frac{r}{2}\) feet. In terms of r, what is the area of the sidewalk?
A. \(2 \pi r^2\)
B. \(\frac{5 \pi r^2}{4}\)
C. \(\frac{9 \pi r^2}{4}\)
D. \(\pi r^2\)
E. \(\frac{\pi r^2}{2}\)
A. \(2 \pi r^2\)
B. \(\frac{5 \pi r^2}{4}\)
C. \(\frac{9 \pi r^2}{4}\)
D. \(\pi r^2\)
E. \(\frac{\pi r^2}{2}\)
Radius of pool = \(r\)
Radius of sidewalk = \(\frac{r}{2}\)
Radius of the pool with sidewalk= \(r + \frac{r}{2} = \frac{3r}{2}\)
Area of sidewalk = Area of pool with sidewalk - Area of pool
= \(π (\frac{3r}{2})^2\) - \(π r^2\)
= \(\frac{{9 π r^2}}{4} - \frac{{4 π r^2}}{4}\)
= \(\frac{{5 π r^2}}{4}\)
Hence, option B
gmatclubot
A circular pool of radius r feet is surrounded by a circular sidewalk [#permalink]
18 Feb 2021, 01:06
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