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

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

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New post 22 Feb 2018, 19:51
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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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New post 22 Feb 2018, 21:04
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


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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New post 22 Feb 2018, 21:22
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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New post 23 Feb 2018, 01:04
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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Re: A magician wants to ship a magic wand to the location of his next sho  [#permalink]

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New post 23 Feb 2018, 01:15
Answer is (D).
The longest cylinder that can be accommodated in the box is the length of its main diagonal.

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Re: A magician wants to ship a magic wand to the location of his next sho &nbs [#permalink] 23 Feb 2018, 01:15
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