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# If the radius of a circle were increased by 5 feet, the area of the

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Math Expert
Joined: 02 Sep 2009
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If the radius of a circle were increased by 5 feet, the area of the [#permalink]

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21 Nov 2017, 23:12
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If the radius of a circle were increased by 5 feet, the area of the circular region would increase by 65π square feet. What is the radius, in feet, before the increase?

(A) 4
(B) 8
(C) 9
(D) 13
(E) 18
[Reveal] Spoiler: OA

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Re: If the radius of a circle were increased by 5 feet, the area of the [#permalink]

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22 Nov 2017, 08:27
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Bunuel wrote:
If the radius of a circle were increased by 5 feet, the area of the circular region would increase by 65π square feet. What is the radius, in feet, before the increase?

(A) 4
(B) 8
(C) 9
(D) 13
(E) 18

Let r = radius of ORIGINAL circle
So, area of ORIGINAL circle = πr²

If the radius of a circle were increased by 5 feet....
So, r + 5 = radius of NEW circle
Area of NEW circle = π(r + 5)²

...the area of the circular region would increase by 65π square feet.
(area of NEW circle) = (area of ORIGINAL circle) + 65π
In other words, π(r + 5)² = πr² + 65π
Divide both sides by π to get: (r + 5)² = r² + 65
Expand and simplify left side: r² + 10r + 25 = r² + 65
Subtract r² from both sides to get: 10r + 25 = 65
Subtract 25 from both sides to get: 10r = 40
Solve: r = 4

What is the radius, in feet, before the increase?
= A

Cheers,
Brent
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If the radius of a circle were increased by 5 feet, the area of the [#permalink]

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22 Nov 2017, 09:15
Bunuel wrote:
If the radius of a circle were increased by 5 feet, the area of the circular region would increase by 65π square feet. What is the radius, in feet, before the increase?

(A) 4
(B) 8
(C) 9
(D) 13
(E) 18

Another way: use the answer choices.

$$r = 9$$
Original area: $$πr^2 = 81π$$

New radius: $$(9 + 5) = 14$$
New area: $$196π$$

Difference: $$(196 - 81)π = 115π$$

That difference is too great by a lot -- almost twice 65π. Eliminate Answers D and E (the gap between difference of squares increases as numbers get larger, and we're adding the same constant).

Answer B, r = 8, is too close to 9. Try Answer (A)

Original $$r = 4$$
Original area = $$16π$$

New radius: $$(4 + 5) = 9$$
New area: $$81π$$

Difference: $$(81π - 16π) = 65π$$
That's a match.

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Re: If the radius of a circle were increased by 5 feet, the area of the [#permalink]

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23 Nov 2017, 00:13
Hey guys what is the OA? Is it A?
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Math Expert
Joined: 02 Sep 2009
Posts: 44600
Re: If the radius of a circle were increased by 5 feet, the area of the [#permalink]

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23 Nov 2017, 00:32
NEENA SHEREEN wrote:
Hey guys what is the OA? Is it A?

The OA will be automatically revealed on Tuesday 28th of November 2017 10:12:20 PM Pacific Time Zone
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Re: If the radius of a circle were increased by 5 feet, the area of the   [#permalink] 23 Nov 2017, 00:32
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