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The circular pool in the figure above has a tile border 3 feet wide (t
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Updated on: 05 Nov 2021, 07:11
Updated on: 05 Nov 2021, 07:11
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The circular pool in the figure above has a tile border 3 feet wide (the white area surrounding the pool) and the area, in square feet, of the pool and tile included is 225π. What is the area, in square feet, of the pool that excludes the tile border?
A. 12π
B. 24π
C. 81π
D. 144π
E. 156π
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GRE The circular pool in the figure above.jpg [ 18.32 KiB | Viewed 1832 times ]
Re: The circular pool in the figure above has a tile border 3 feet wide (t
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05 Nov 2021, 07:13
05 Nov 2021, 07:13
1
We are given the area of the pool with the tile included, as well as the size of the tile border.
So with the tile border, the area of the pool is \(225π\), meaning that the length of the radius is \(15\) (because the area of a circle is \(πr^2\), we take the square root of \(225\) to find the radius). \(\sqrt{225} = 15\).
If the radius of the pool and tile is \(15\), and the tile border is \(3\) feet wide, then the radius of the pool alone is \(15 - 3 = 12\).
With this info, we can find the area of the pool alone using the formula for the area of a circle.
Area of circle \(= πr^2\)
\(π12^2 = 144π\) = area of the pool
Answer D
So with the tile border, the area of the pool is \(225π\), meaning that the length of the radius is \(15\) (because the area of a circle is \(πr^2\), we take the square root of \(225\) to find the radius). \(\sqrt{225} = 15\).
If the radius of the pool and tile is \(15\), and the tile border is \(3\) feet wide, then the radius of the pool alone is \(15 - 3 = 12\).
With this info, we can find the area of the pool alone using the formula for the area of a circle.
Area of circle \(= πr^2\)
\(π12^2 = 144π\) = area of the pool
Answer D
Re: The circular pool in the figure above has a tile border 3 feet wide (t
[#permalink]
26 Jun 2024, 16:24
26 Jun 2024, 16:24
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