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An open box in the shape of a cube measuring 50 centimeters on each si

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An open box in the shape of a cube measuring 50 centimeters on each si  [#permalink]

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New post 30 Jul 2018, 22:04
2
1
22
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (02:07) correct 33% (02:07) wrong based on 553 sessions

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An open box in the shape of a cube measuring 50 centimeters on each side is constructed from plywood. If the plywood weighs 1.5 grams per square centimeter, which of the following is closest to the total weight, in kilograms, of the plywood used for the box? (1 kilogram = 1,000 grams)

A. 2
B. 4
C. 8
D. 13
E. 19

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Re: An open box in the shape of a cube measuring 50 centimeters on each si  [#permalink]

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New post 30 Jul 2018, 22:25
2
3

Solution



Given:
    • An open box in the shape of a cube measuring 50 cm on each side is constructed from plywood
    • Plywood weighs 1.5 grams per square cm
    • 1 kilogram = 1,000 grams

To find:
    • The closest value, of the total weight, in kilograms, of the plywood used for the box

Approach and Working:
As it is an open box, we are assuming that there will be only 5 surfaces made of plywood.
    • Area of each surface = 50 * 50 sq. cm.
    • So, area of 5 surfaces = 5 * 50 * 50 sq. cm.
    • Therefore, total weight = 5 * 50 * 50 * 1.5 grams = 18750 grams = 18.75 kg

Hence, the correct answer is option E.

Answer: E
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Re: An open box in the shape of a cube measuring 50 centimeters on each si  [#permalink]

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New post 31 Jul 2018, 02:39
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Bunuel wrote:
An open box in the shape of a cube measuring 50 centimeters on each side is constructed from plywood. If the plywood weighs 1.5 grams per square centimeter, which of the following is closest to the total weight, in kilograms, of the plywood used for the box? (1 kilogram = 1,000 grams)


Surface area of each side = 50 * 50
Surface area of all sides = 5 * 50 * 50 (since it is an open box, sixth side will be missing)

weight of the box in gms = 5 * 50 * 50 * 1.5 = 18750 = 19000(approx)
weight of the box in Kgms = 19000 / 1000 = 19

Hence, E.
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Re: An open box in the shape of a cube measuring 50 centimeters on each si  [#permalink]

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New post 10 Aug 2018, 19:14
Bunuel wrote:
An open box in the shape of a cube measuring 50 centimeters on each side is constructed from plywood. If the plywood weighs 1.5 grams per square centimeter, which of the following is closest to the total weight, in kilograms, of the plywood used for the box? (1 kilogram = 1,000 grams)

A. 2
B. 4
C. 8
D. 13
E. 19


If the open box is in the shape of a cube measuring 50 centimeters on each side, then it has five faces, each measuring 50^2 = 2500 square centimeters, and thus its surface area is 5 x 2500 = 12,500 square centimeters. Since each square centimeter of plywood weighs 1.5 grams, the plywood needed to constructed the open box is 12,500 x 1.5 = 18,750 grams or 18.75 kilograms.

Answer: E
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Re: An open box in the shape of a cube measuring 50 centimeters on each si  [#permalink]

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New post 28 Jun 2019, 05:44
I agree with the explanations above.

However, I am surprised that the GMAC did not take the opportunity to include something like 22.5 in the answer choices to set a trap for the people who forgot that the box only consists of 5 parts of wood due to being open at the top. :)
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Re: An open box in the shape of a cube measuring 50 centimeters on each si   [#permalink] 28 Jun 2019, 05:44
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