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In a windowless cube-shaped storage room, the ceiling and 4 walls, inc

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Bunuel
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In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink] New post   30 Nov 2017, 23:49
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In a windowless cube-shaped storage room, the ceiling and 4 walls, including a door, are completely painted. The floor is not painted. If the painted area is equal to 80 square meters, what is the volume of the room, in cubic meters?

(A) 16
(B) 20
(C) 64
(D) 256
(E) 400
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C
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pushpitkc
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Re: In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink] New post   01 Dec 2017, 12:57
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Bunuel wrote:
In a windowless cube-shaped storage room, the ceiling and 4 walls, including a door, are completely painted. The floor is not painted. If the painted area is equal to 80 square meters, what is the volume of the room, in cubic meters?

(A) 16
(B) 20
(C) 64
(D) 256
(E) 400


The windowless cube-shaped room is painted excluding the floor.
Therefore, 5 of the 6 faces of the cube have been painted.
Each face of the cube has an area of \(side^2\), making total area of \(5*side^2\)

Because the painted area is 80 sq meters, \(5*side^2 = 80 => side =\sqrt{16} = 4\)

The volume of the cube, is \(side^3\) = 64(Option C)
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generis
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In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink] New post   Updated on: 01 Dec 2017, 13:22
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Bunuel wrote:
In a windowless cube-shaped storage room, the ceiling and 4 walls, including a door, are completely painted. The floor is not painted. If the painted area is equal to 80 square meters, what is the volume of the room, in cubic meters?

(A) 16
(B) 20
(C) 64
(D) 256
(E) 400

Five of the six surfaces are painted, that is
\(\frac{5}{6}\) of total surface area is painted
Total painted area = 80 sq m

Surface area = \(6s^2\)

\(\frac{5}{6}(6s^2) = 80\)

\(6s^2 = (80) * \frac{6}{5}\)

\(6s^2 = 96\)
\(s^2 = 16\)
\(s = 4\)

Volume in cubic meters
\(s^3 = 4^3 =\)
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64


Answer
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C


Edited, answer has changed, because previously I used the formula for area of a square rather than volume of a cube. :roll: Sorry! Thanks, pushpitkc. I'll put my kudos on your post below.

Originally posted by generis on 01 Dec 2017, 10:51.
Last edited by generis on 01 Dec 2017, 13:22, edited 1 time in total.
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Re: In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink] New post   01 Dec 2017, 11:17
Bunuel wrote:
In a windowless cube-shaped storage room, the ceiling and 4 walls, including a door, are completely painted. The floor is not painted. If the painted area is equal to 80 square meters, what is the volume of the room, in cubic meters?

(A) 16
(B) 20
(C) 64
(D) 256
(E) 400


The surface area of a cube without floor is four walls + ceiling => \(4a^2 + a^2 = 5a^2\)
\(5a^2 = 80\)
\(a^2 = 16\)
\(a= 4\)

The Volume of the room is \(a^3 = 64\)
Hence, the answer is C
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Re: In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink]
01 Dec 2017, 11:17
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