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# A rectangular box with a square base contains 6 cubic feet. If the hei

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Math Expert
Joined: 02 Sep 2009
Posts: 50039
A rectangular box with a square base contains 6 cubic feet. If the hei  [#permalink]

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11 Mar 2018, 21:32
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15% (low)

Question Stats:

86% (01:54) correct 14% (01:19) wrong based on 27 sessions

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A rectangular box with a square base contains 6 cubic feet. If the height of the box is 18 inches, how many feet are there in each side of the base? (1 foot = 12 inches)

(A) 1

(B) 2

(C) $$\sqrt{3}$$

(D) $$\frac{\sqrt{3}}{3}$$

(E) 4

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Re: A rectangular box with a square base contains 6 cubic feet. If the hei  [#permalink]

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12 Mar 2018, 02:05
Bunuel wrote:
A rectangular box with a square base contains 6 cubic feet. If the height of the box is 18 inches, how many feet are there in each side of the base?

(A) 1

(B) 2

(C) $$\sqrt{3}$$

(D) $$\frac{\sqrt{3}}{3}$$

(E) 4

Here, we need to know that 1 feet = 12 inches

Since the rectangular box has a square base, assume length = breadth = x

We know that the height of this box is 18 inches or $$\frac{3}{2}$$ft and the volume of the box is $$6$$

$$\frac{3x^2}{2} = 6$$ -> $$x^2 = \frac{2*6}{3} = 4$$ -> x = $$\sqrt{4} = 2$$

Therefore, the rectangular box is 2 feet(Option B) at each side of the base
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Re: A rectangular box with a square base contains 6 cubic feet. If the hei  [#permalink]

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12 Mar 2018, 06:26
Bunuel wrote:
A rectangular box with a square base contains 6 cubic feet. If the height of the box is 18 inches, how many feet are there in each side of the base?

(A) 1

(B) 2

(C) $$\sqrt{3}$$

(D) $$\frac{\sqrt{3}}{3}$$

(E) 4

Volume of cube = $$a*a*h = 6$$

i.e. $$a^2 = 6/(18/12)$$

i.e. a = √4 = 2

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Re: A rectangular box with a square base contains 6 cubic feet. If the hei  [#permalink]

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13 Mar 2018, 16:53
Bunuel wrote:
A rectangular box with a square base contains 6 cubic feet. If the height of the box is 18 inches, how many feet are there in each side of the base?

(A) 1

(B) 2

(C) $$\sqrt{3}$$

(D) $$\frac{\sqrt{3}}{3}$$

(E) 4

A box with a square base has a volume of V = s^2 * h where s is the side length of the square base and h is the height of the box. Since 18 inches = 1.5 feet, we have:

6 = s^2 * 1.5

4 = s^2

s = 2 feet

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Re: A rectangular box with a square base contains 6 cubic feet. If the hei &nbs [#permalink] 13 Mar 2018, 16:53
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