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Jack is storing a rectangular box inside a cylindrical conta
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25 Nov 2020, 09:38

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Jack is storing a rectangular box inside a cylindrical container. The container has a volume of \(980\pi\) cubic inches and a height of 20 inches. Which of the following dimensions could the box have in order to fit inside the cylinder?

Indicate all such values.

A. 3 inches by 6 inches by 12 inches

B. 6 inches by 9 inches by 15 inches

C. 10 inches by 10 inches by 10 inches

D. 8 inches by 9 inches by 16 inches

E. 11 inches by 15 inches by 18 inches

F. 9 inches by 9 inches by 20 inches

Indicate all such values.

A. 3 inches by 6 inches by 12 inches

B. 6 inches by 9 inches by 15 inches

C. 10 inches by 10 inches by 10 inches

D. 8 inches by 9 inches by 16 inches

E. 11 inches by 15 inches by 18 inches

F. 9 inches by 9 inches by 20 inches

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Official Answer

A,B,D,F

Re: Jack is storing a rectangular box inside a cylindrical conta
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27 Nov 2020, 00:03

5

Carcass wrote:

Jack is storing a rectangular box inside a cylindrical container. The container has a volume of \(980\pi\) cubic inches and a height of 20 inches. Which of the following dimensions could the box have in order to fit inside the cylinder?

Indicate all such values.

A. 3 inches by 6 inches by 12 inches

B. 6 inches by 9 inches by 15 inches

C. 10 inches by 10 inches by 10 inches

D. 8 inches by 9 inches by 16 inches

E. 11 inches by 15 inches by 18 inches

F. 9 inches by 9 inches by 20 inches

Indicate all such values.

A. 3 inches by 6 inches by 12 inches

B. 6 inches by 9 inches by 15 inches

C. 10 inches by 10 inches by 10 inches

D. 8 inches by 9 inches by 16 inches

E. 11 inches by 15 inches by 18 inches

F. 9 inches by 9 inches by 20 inches

After some pondering, this is what I got!

Let's say that the diagonal of the rectangular box is equal to the diagonal of the cylinder, which is \(14\)

taking least of the two values from each option and trying to see if it fits

Option A -> \(3^2 + 6^2 <= 14^2\)

Option B -> \(6^2 + 9^2 <=14^2 \)

Option C -> \(10^2 + 10^2 > 14^2\) --> It is greater. Cannot be fit into the cylinder

Option D -> \(8^2 + 9^2 <= 14^2\)

Option E -> \(11^2 + 15^2 > 14^2\) --> It is greater.Cannot be fit into the cylinder

Option F -> \(9^2 + 9^2 <= 14^2\)

Re: Jack is storing a rectangular box inside a cylindrical conta
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26 Nov 2020, 05:09

1

Jack is storing a rectangular box inside a cylindrical container. The container has a volume of 980π cubic inches and a height of 20 inches. Which of the following dimensions could the box have in order to fit inside the cylinder?

using the volume's formula for cylinder r=7

assume a rectangular is inscribed in a circle with a radius of 7. each side of the rectangular is 7radi2

now the area of rectangular with sides of 7radi2 is 98. and the volume of box is 98*20=1960

check the answer choices that their products is 1960 or less and the product of two of them is less than 98

using the volume's formula for cylinder r=7

assume a rectangular is inscribed in a circle with a radius of 7. each side of the rectangular is 7radi2

now the area of rectangular with sides of 7radi2 is 98. and the volume of box is 98*20=1960

check the answer choices that their products is 1960 or less and the product of two of them is less than 98

Re: Jack is storing a rectangular box inside a cylindrical conta
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28 Nov 2020, 23:17

here, h=20, r=7=> d=14

as the height of the cylinder is 20 inches, we can fit a rectangular box having a height atmost= 20 inches

the maximum length and/or width of the rectangular box can be, x= 7* sqrt(2)=9.87 (approx)

[d^2= x^2+x^2=>x=7*sqrt(2)]

therefore, the box will be such that it's length, l<=9.87; width, W<=9.87 and height, H<=20

only A, B, D and F fulfil the above conditions.

as the height of the cylinder is 20 inches, we can fit a rectangular box having a height atmost= 20 inches

the maximum length and/or width of the rectangular box can be, x= 7* sqrt(2)=9.87 (approx)

[d^2= x^2+x^2=>x=7*sqrt(2)]

therefore, the box will be such that it's length, l<=9.87; width, W<=9.87 and height, H<=20

only A, B, D and F fulfil the above conditions.

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Re: Jack is storing a rectangular box inside a cylindrical conta
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29 Nov 2020, 07:45

3

The cylinder has height =20, diameter, d=14 [πr2h=980π ⟹ r =7]

So, the rectangle height must be ≤ 20

And the face diagonal of another two side must be less than or equal diameter

√ (w^2+L^2) ≤ 14

0r w^2+L^2≤196

A. 3^2+6^2=45

B. 6^2 +9^2=117

C. 10^2 +10^2=200

D. 8^2 +9^2=145

E. 11^2 +15^2=346

F. 92 +92=162

Answer: ABDF

So, the rectangle height must be ≤ 20

And the face diagonal of another two side must be less than or equal diameter

√ (w^2+L^2) ≤ 14

0r w^2+L^2≤196

A. 3^2+6^2=45

B. 6^2 +9^2=117

C. 10^2 +10^2=200

D. 8^2 +9^2=145

E. 11^2 +15^2=346

F. 92 +92=162

Answer: ABDF

Re: Jack is storing a rectangular box inside a cylindrical conta
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12 Jun 2024, 11:23

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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12 Jun 2024, 11:23
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