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If the circumference of a circle inscribed in a square is 25π, what is

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If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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New post 22 Jun 2018, 01:27
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E

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Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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New post 22 Jun 2018, 02:13
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Answer is E.

Diameter of circle = Side of square.
Let diameter be d and side be s.
Circumference = πd = 25π
So, d = 25 = s.
Perimeter = 4s = 100

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Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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New post 22 Jun 2018, 02:13
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πD = 25π => diameter is 25.
Therefore, side of square = 25.
Perimeter = 4*side = 100

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Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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New post 22 Jun 2018, 04:39

Solution



Given:
    • The circumference of a circle inscribed in a square is 25π

To find:
    • The perimeter of the square

Approach and Working:
When a circle is inscribed in a square, the diameter of the circle is equal to the length of the side of the square

Image

If r is the radius of the circle, then
    • 2πr = 25π
    Or, 2r = 25

Therefore, we can say, length of the side of the square = 25
    • Perimeter of the square = 25 * 4 = 100

Hence, the correct answer is option E.

Answer: E
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Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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New post 23 Jun 2018, 09:10
Top Contributor
Bunuel wrote:
If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?


A. 20

B. 25

C. 40

D. 50

E. 100


We have the following:
Image

The perimeter of the circle = 25π

We can see that the perimeter of the square is GREATER THAN the perimeter of the circle

25π ≈ (25)(3) ≈ 75
So, the perimeter of the square is GREATER THAN 25π

Check the answer choices....only one answer choice works.

Answer: E

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Brent
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Re: If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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New post 27 Jun 2018, 18:06
Bunuel wrote:
If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?


A. 20

B. 25

C. 40

D. 50

E. 100


When a circle is inscribed in a square, the diameter of the circle is equal to the side of the square.

Since circumference = πd, we have:

πd = 25π

d = 25 = side of the square

Thus, the perimeter of the square is 25 x 4 = 100.

Answer: E
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If the circumference of a circle inscribed in a square is 25π, what is  [#permalink]

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New post 18 Mar 2019, 13:37
[1] Find Diameter

Since the diameter of a circle is equal to the side of a square, finding the circle's diameter will allow us to calculate the square's perimeter.

\(Circumference = Diameter \times \pi\)

\(\frac{25\pi}{\pi} = Diameter\)

\(Diameter = 25\)

[2] Calculate Perimeter


\(Perimeter = 4 \times Side\)

\(Side \equiv Diameter\)

\(25\times 4 = 100\)

Answer E
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If the circumference of a circle inscribed in a square is 25π, what is   [#permalink] 18 Mar 2019, 13:37
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