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If the radius of a circle were increased by 5 feet, the area of the ci
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10 Jun 2021, 08:53
10 Jun 2021, 08:53
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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
(A) 4
(B) 8
(C) 9
(D) 13
(E) 18
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Re: If the radius of a circle were increased by 5 feet, the area of the ci
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10 Jun 2021, 09:08
10 Jun 2021, 09:08
1
Carcass 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
(A) 4
(B) 8
(C) 9
(D) 13
(E) 18
Let r = radius of ORIGINAL circle
Area = π(radius)²
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?
Answer = 4
= A
Cheers,
Brent
gmatclubot
Re: If the radius of a circle were increased by 5 feet, the area of the ci [#permalink]
10 Jun 2021, 09:08
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