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The greatest possible distance between any two points on the surface o

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Carcass
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The greatest possible distance between any two points on the surface o [#permalink] New post   22 Mar 2022, 02:00
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90% (01:53) correct 10% (01:58) wrong based on 10 sessions

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The greatest possible distance between any two points on the surface of a cube is \(3 \sqrt{6}\). What is the total surface area of the cube?

36
\(27 \sqrt{3}\)
72
\(54 \sqrt{2}\)
108
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E
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Re: The greatest possible distance between any two points on the surface o [#permalink] New post   28 Mar 2022, 01:11
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Carcass wrote:
The greatest possible distance between any two points on the surface of a cube is \(3 \sqrt{6}\). What is the total surface area of the cube?

36
\(27 \sqrt{3}\)
72
\(54 \sqrt{2}\)
108


Diagonal of a cube is the greatest distance between any 2 points on a cube
Diagonal of cube with edge length \(a\) is \(a\sqrt{3}\)

\(a\sqrt{3} = 3\sqrt{6}\)
\(a = \frac{3\sqrt{6}}{\sqrt{3}} = \frac{3(\sqrt{2})(\sqrt{3})}{\sqrt{3}} = 3\sqrt{2}\)

TSA = \(6a^2 = 6(3\sqrt{2})^2 = (6)(18) = 108\)

Hence, option E
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Re: The greatest possible distance between any two points on the surface o [#permalink]
28 Mar 2022, 01:11
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