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

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Math Expert
Joined: 02 Sep 2009
Posts: 42649

Kudos [?]: 135955 [1], given: 12717

In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink]

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30 Nov 2017, 22:49
1
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Question Stats:

81% (00:27) correct 19% (00:05) wrong based on 16 sessions

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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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135955 [1], given: 12717

VP
Joined: 22 May 2016
Posts: 1137

Kudos [?]: 407 [0], given: 647

In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink]

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01 Dec 2017, 09:51
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
$$s^3 = 4^3 =$$
[Reveal] Spoiler:
64

[Reveal] Spoiler:
C

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

Last edited by genxer123 on 01 Dec 2017, 12:22, edited 1 time in total.

Kudos [?]: 407 [0], given: 647

Intern
Joined: 15 Oct 2017
Posts: 27

Kudos [?]: 3 [0], given: 57

Location: Ireland
Concentration: Healthcare, Finance
Re: In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink]

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01 Dec 2017, 10:17
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 $$a^3 = 64$$

Kudos [?]: 3 [0], given: 57

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1710

Kudos [?]: 754 [1], given: 20

Location: India
WE: Sales (Retail)
Re: In a windowless cube-shaped storage room, the ceiling and 4 walls, inc [#permalink]

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01 Dec 2017, 11:57
1
KUDOS
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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Kudos [?]: 754 [1], given: 20

Re: In a windowless cube-shaped storage room, the ceiling and 4 walls, inc   [#permalink] 01 Dec 2017, 11:57
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