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# A magician wants to ship a magic wand to the location of his next sho

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Math Expert
Joined: 02 Sep 2009
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A magician wants to ship a magic wand to the location of his next sho  [#permalink]

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22 Feb 2018, 20:51
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25% (medium)

Question Stats:

77% (01:27) correct 23% (02:02) wrong based on 56 sessions

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A magician wants to ship a magic wand to the location of his next show. The rectangular box he has available for this purpose measures 6 inches wide by 8 inches long by 10 inches high. What is the longest cylindrical wand of negligible diameter that can be shipped in this box?

(A) 10 inches

(B) $$8\sqrt{2}$$ inches

(C) $$8\sqrt{3}$$ inches

(D) $$10\sqrt{2}$$ inches

(E) $$10\sqrt{3}$$ inches

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Re: A magician wants to ship a magic wand to the location of his next sho  [#permalink]

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22 Feb 2018, 22:04
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Bunuel wrote:
A magician wants to ship a magic wand to the location of his next show. The rectangular box he has available for this purpose measures 6 inches wide by 8 inches long by 10 inches high. What is the longest cylindrical wand of negligible diameter that can be shipped in this box?

(A) 10 inches

(B) $$8\sqrt{2}$$ inches

(C) $$8\sqrt{3}$$ inches

(D) $$10\sqrt{2}$$ inches

(E) $$10\sqrt{3}$$ inches

The box in which the magician wants to shift his magic wand is a cuboid.
The maximum height of the magic wand that can be shipped in the box is
the distance of the diagonal.

The diagonal can be calculated using the formulae $$\sqrt{Length^2 + Breadth^2 + Height^2} = \sqrt{36 + 64 + 100} = \sqrt{200} = 10\sqrt{2}$$

Therefore, the longest cylindrical wand of negligible diameter will be $$10\sqrt{2}$$ (Option D)
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A magician wants to ship a magic wand to the location of his next sho  [#permalink]

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22 Feb 2018, 22:22
We can find the solution using the diagonal of a rectangle formula -$$\sqrt{36+64+100}$$ = $$\sqrt{200}$$ = 10$$\sqrt{2}$$

Ans: 10$$\sqrt{2}$$
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Re: A magician wants to ship a magic wand to the location of his next sho  [#permalink]

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23 Feb 2018, 02:04
Bunuel wrote:
A magician wants to ship a magic wand to the location of his next show. The rectangular box he has available for this purpose measures 6 inches wide by 8 inches long by 10 inches high. What is the longest cylindrical wand of negligible diameter that can be shipped in this box?

(A) 10 inches

(B) $$8\sqrt{2}$$ inches

(C) $$8\sqrt{3}$$ inches

(D) $$10\sqrt{2}$$ inches

(E) $$10\sqrt{3}$$ inches

given box is a cuboid

length of diagonal = rt l^2 + b^2 + h^ 2
= rt 36+64+100 = rt200 = 10 rt2

(D) imo
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Joined: 23 Feb 2018
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Re: A magician wants to ship a magic wand to the location of his next sho  [#permalink]

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23 Feb 2018, 02:15
The longest cylinder that can be accommodated in the box is the length of its main diagonal.

Posted from GMAT ToolKit
Re: A magician wants to ship a magic wand to the location of his next sho   [#permalink] 23 Feb 2018, 02:15
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