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# How deep will the sand be in a rectanglular sandbox with inside dimens

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Joined: 02 Sep 2009
Posts: 53865
How deep will the sand be in a rectanglular sandbox with inside dimens  [#permalink]

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04 Dec 2017, 08:03
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Difficulty:

25% (medium)

Question Stats:

69% (01:11) correct 31% (00:53) wrong based on 42 sessions

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How deep will the sand be in a rectanglular sandbox with inside dimensions 300 centimeters long, 200 centimeters wide, and 20 centimeters deep if 600,000 cubic centimeters of sand is evenly distributed in it?

(A) 1 cm
(B) 2 cm
(C) 10 cm
(D) 12 cm
(E) 20 cm

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How deep will the sand be in a rectanglular sandbox with inside dimens  [#permalink]

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04 Dec 2017, 09:35
Bunuel wrote:
How deep will the sand be in a rectanglular sandbox with inside dimensions 300 centimeters long, 200 centimeters wide, and 20 centimeters deep if 600,000 cubic centimeters of sand is evenly distributed in it?

(A) 1 cm
(B) 2 cm
(C) 10 cm
(D) 12 cm
(E) 20 cm

The volume of the rectangular sandbox is 300*200*20.

Since, there is 600000 cubic cms evenly distributed in the sand,
$$\frac{600000}{300*200*20} = \frac{10}{20} = \frac{1}{2}$$ of the sand box is filled.

Therefore, the depth of sand in the rectangular sandbox is $$\frac{1}{2}*20$$ cm(which is the total depth) = 10cm(Option C)
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Re: How deep will the sand be in a rectanglular sandbox with inside dimens  [#permalink]

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04 Dec 2017, 22:37
The Volume of the box V = 1200000; The Volume of sand V1 = 600000;

Which means, about half the box is filled with sand. Which leads to 10 cms of the box being filled.

V1/V = 1/2; 1/2 (20) = 10 cms
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Re: How deep will the sand be in a rectanglular sandbox with inside dimens  [#permalink]

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11 Jan 2018, 15:01
Bunuel wrote:
How deep will the sand be in a rectanglular sandbox with inside dimensions 300 centimeters long, 200 centimeters wide, and 20 centimeters deep if 600,000 cubic centimeters of sand is evenly distributed in it?

(A) 1 cm
(B) 2 cm
(C) 10 cm
(D) 12 cm
(E) 20 cm

If the sand is evenly distributed in a sand box, then its height should be:

600,000/(300 x 200) = 600,000/60,000 = 10 cm

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Re: How deep will the sand be in a rectanglular sandbox with inside dimens   [#permalink] 11 Jan 2018, 15:01
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