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# There is a rectangular solid such that the total surface area is 600

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There is a rectangular solid such that the total surface area is 600  [#permalink]

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15 Nov 2019, 13:12
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There is a rectangular solid such that the total surface area is 600 and the rectangular solid consists of n small cubes with its volume 8. What is the greatest value of n?

A. 85 B. 100 C. 125 D. 200 E. 225

Hello all!
I couldn't figure out how to approach this geometry problem without making it too complicated.

Thank you!
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There is a rectangular solid such that the total surface area is 600  [#permalink]

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Updated on: 16 Nov 2019, 00:50
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1
The dimensions of the rectangular box must be 10 X 10 X 6, and each side of cube is 2 , so we have 5 boxes on the length's side x 2 sides containing 5-5 boxes each, i.e 25 boxes , 5 on width , hence 5 X 5 X 5 = 125.
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Originally posted by Abhi077 on 15 Nov 2019, 13:53.
Last edited by Abhi077 on 16 Nov 2019, 00:50, edited 1 time in total.
Intern
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There is a rectangular solid such that the total surface area is 600  [#permalink]

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15 Nov 2019, 14:46
1
Well, I think I've got this one.

To find the greatest value of N we need the greatest possible volume.

Given that hl+hw+lw = 300, the greatest possible volume must have 3 equal lengths ( 5*5*5 is bigger than 5*4*6 and so on)

300/3 = 100, so we assume that each of hl, hw, and lw is 100, so each equal side = 10 and the maximum volume = 1000. Finding the maximum volume just divide it by 8 (hlw/8 = n) and you have the result. C
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Re: There is a rectangular solid such that the total surface area is 600  [#permalink]

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15 Nov 2019, 21:04
Bunuel Can you provide the solution for this?
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Re: There is a rectangular solid such that the total surface area is 600  [#permalink]

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15 Nov 2019, 23:32
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ec9rs wrote:
There is a rectangular solid such that the total surface area is 600 and the rectangular solid consists of n small cubes with its volume 8. What is the greatest value of n?

A. 85 B. 100 C. 125 D. 200 E. 225

Hello all!
I couldn't figure out how to approach this geometry problem without making it too complicated.

Thank you!

Greatest value of n is calculated when all the sides of the rectangular solid are equal.
hence, considering rectangular solid as cube

6a^2 = 600
a =10

Volume of cube = 1000 = 8 n
n = 125
C is correct
Re: There is a rectangular solid such that the total surface area is 600   [#permalink] 15 Nov 2019, 23:32
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