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555-605 (Medium)|   Geometry|               
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diagonal of square= √2
and diamater = √2
so when sides are up radius √2/2
IMO B


Bunuel

The figure above shows a drop-leaf table. With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle. What is the radius, in meters, of the tabletop when all four leaves are up?

A. 1/2

B. \(\frac{\sqrt{2}}{2}\)

C. 1

D. \(\sqrt{2}\)

E. 2


PS26602.01
Quantitative Review 2020 NEW QUESTION


Attachment:
2019-04-26_1803.png
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DavidTutorexamPAL
Bunuel

The figure above shows a drop-leaf table. With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle. What is the radius, in meters, of the tabletop when all four leaves are up?


A. 1/2

B. \(\frac{\sqrt{2}}{2}\)

C. 1

D. \(\sqrt{2}\)

E. 2



PS26602.01
Quantitative Review 2020 NEW QUESTION


Attachment:
2019-04-26_1803.png

We can use simple geometric rules to solve this problem, a Precise approach.
The radius of the circle is half its diameter. Since the diameter of the circle is just the diagonal of the (square) tabletop, and since the diagonal of a square with a side of 1 is sqrt(2) (remember your 45-45-90 triangle!), then our answer is 1/2 * sqrt(2).

(B) is our answer.

I can't visualize the question.
Please explain with drawing. Thanks

Posted from my mobile device
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shaonkarim
DavidTutorexamPAL

We can use simple geometric rules to solve this problem, a Precise approach.
The radius of the circle is half its diameter. Since the diameter of the circle is just the diagonal of the (square) tabletop, and since the diagonal of a square with a side of 1 is sqrt(2) (remember your 45-45-90 triangle!), then our answer is 1/2 * sqrt(2).

(B) is our answer.

I can't visualize the question.
Please explain with drawing. Thanks

Posted from my mobile device
Hey shaonkarim

See the attached drawing.
BD is the diameter of the circle and also the diagonal of the square.
Since the side of the square is 1, then BD is sqrt(2) so the radius is 1/2 * sqrt(2)

Hope this helps!
Attachments

pic.png
pic.png [ 15.48 KiB | Viewed 22964 times ]

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Bunuel

The figure above shows a drop-leaf table. With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle. What is the radius, in meters, of the tabletop when all four leaves are up?

A. 1/2

B. \(\frac{\sqrt{2}}{2}\)

C. 1

D. \(\sqrt{2}\)

E. 2


PS26602.01
Quantitative Review 2020 NEW QUESTION


Attachment:
2019-04-26_1803.png

We see that when the leaves are fully extended, the diameter of the circle is the diagonal of the square. Since the side of the square is 1, then its diagonal is √2. Therefore, the diameter is also √2, and hence the radius is √2/2.

Answer: B
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The sooner you realise the shape is just a square inscribed in a circle, the easier your life becomes.
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Bunuel

The figure above shows a drop-leaf table. With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle. What is the radius, in meters, of the tabletop when all four leaves are up?

A. 1/2

B. \(\frac{\sqrt{2}}{2}\)

C. 1

D. \(\sqrt{2}\)

E. 2


PS26602.01
Quantitative Review 2020 NEW QUESTION


Attachment:
The attachment 2019-04-26_1803.png is no longer available

Actually, this is a square inscribed in a circle.

We need to figure out the diagonal of the square and half the diagonal will be the radius of the circle.

Side of the Square is \(1\) so, the diagonal will be \(1\sqrt{2}\) \(= \) \(\sqrt{2}\)

Thus the radius is \(\frac{\sqrt{2}}{2}\)

The answer is B.
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Circle.png
Circle.png [ 3.98 KiB | Viewed 17256 times ]

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Bunuel

The figure above shows a drop-leaf table. With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle. What is the radius, in meters, of the tabletop when all four leaves are up?

A. 1/2

B. \(\frac{\sqrt{2}}{2}\)

C. 1

D. \(\sqrt{2}\)

E. 2


PS26602.01
Quantitative Review 2020 NEW QUESTION


Attachment:
2019-04-26_1803.png


Ballparking! Yay!

The radius is half of the diagonal of the square.

Is that longer than the side, the same as the side, or shorter than the side? Shorter. Cool, eliminate C, D, and E.
Is it half as long as the side (if it were, then the side and the diagonal would be equal, which they aren't)? Nahhhh. Eliminate A.

Answer choice B.

No math.

ThatDudeKnowsBallparking
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Diagonal of the square is equal to the diameter of the circle. Since each side of square =1, diagonal = root2*side.
Now a circle inscribing a square share a relationship wherein, diagonal of the square is equal to diameter of the circle.
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File comment: Pfa
356E0357-2447-48F4-989C-05C2D5756E6F.jpeg
356E0357-2447-48F4-989C-05C2D5756E6F.jpeg [ 265.77 KiB | Viewed 6051 times ]

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