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The floor of a rectangular room of 72 square meters area needs to be c

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Bunuel
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The floor of a rectangular room of 72 square meters area needs to be c [#permalink] New post   02 Jun 2020, 05:17
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The floor of a rectangular room of 72 square meters area needs to be covered by a circular carpet that occupies exactly half the area of the floor. What must be the circumference of the carpet in meters?

A. 3√π
B. 6√π
C. 9√π
D. 12√π
E. 15√π
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D
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The floor of a rectangular room of 72 square meters area needs to be c [#permalink] New post   02 Jun 2020, 05:28
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Bunuel wrote:
The floor of a rectangular room of 72 square meters area needs to be covered by a circular carpet that occupies exactly half the area of the floor. What must be the circumference of the carpet in meters?

A. 3√π
B. 6√π
C. 9√π
D. 12√π
E. 15√π


ARea of circle = \((\frac{1}{2})*72 = 36 = πr^2\)

i.e. \(r^2 = 36/π\)

i.e. \(r = 6/√π\)

Circumference \(= 2πr = 2π*(6/√π) = 12√π\)

Answer: Option D
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Re: The floor of a rectangular room of 72 square meters area needs to be c [#permalink] New post   02 Jun 2020, 06:42
The answer is option D. Since the area of the circle= 36 sq. mtrs. And if we apply the formula of area of circle we get πr^2= 36 so r= 6/√π and circumference = 2πr= 2*π*6/√π= 12√π

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Re: The floor of a rectangular room of 72 square meters area needs to be c [#permalink] New post   02 Jun 2020, 07:24
IMO D

Cirlce Area = 1/2(Rectangle Area) = 1/2 * 72 = 36

Let circle radius =r

π(r^2) = 36
==> r = 6/√π

Circumference: 2πr ==> 2 * π * 6/√π = 12√π
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Re: The floor of a rectangular room of 72 square meters area needs to be c [#permalink] New post   02 Jun 2020, 09:57
Bunuel wrote:
The floor of a rectangular room of 72 square meters area needs to be covered by a circular carpet that occupies exactly half the area of the floor. What must be the circumference of the carpet in meters?

A. 3√π
B. 6√π
C. 9√π
D. 12√π
E. 15√π


Area of carpet must be 36

Now, \(πr^2 = 36\)

So, \(r =\frac{ 6}{\sqrt{π}}\)

Hence, circumference of the circle will be \(2πr = 2*\frac{ 6}{\sqrt{π}} = \frac{12}{\sqrt{π}}\) , Answer must be (D)
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Re: The floor of a rectangular room of 72 square meters area needs to be c [#permalink] New post   22 Mar 2021, 09:42
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Bunuel wrote:
The floor of a rectangular room of 72 square meters area needs to be covered by a circular carpet that occupies exactly half the area of the floor. What must be the circumference of the carpet in meters?

A. 3√π
B. 6√π
C. 9√π
D. 12√π
E. 15√π

Solution:

We can create the equation where r is the radius of the circular carpet:

π x r^2 = 72/2

r^2 = 36/π

r = √(36/π) = 6/√π

Therefore, the circumference of the carpet is 2π x 6/√π = 12√π meters.

Answer: D
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Re: The floor of a rectangular room of 72 square meters area needs to be c [#permalink]
22 Mar 2021, 09:42
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