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# A perfectly spherical satellite with a radius of 4 feet is being packe

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Senior RC Moderator
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A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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06 Mar 2017, 22:22
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Difficulty:

75% (hard)

Question Stats:

54% (02:21) correct 46% (02:52) wrong based on 100 sessions

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A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=($$\frac{4}{3}$$ πr^3 .)

(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680

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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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07 Mar 2017, 00:49
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A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=(4/3)pie r^3 .)

(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680

Since the radius of the satellite is 4 feet, the diameter is 8 feet. So the minimum inside dimensions of the crate need to be 8 by 8 by 8.

Since the inside dimensions of the crate are consecutive even integers, the smallest such crate that can be used would have the dimension 8 by 10 by 12.

The volume of such a crate would be 8*10*12 = 960 cubic feet

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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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07 Mar 2017, 11:06
VeritasPrepKarishma wrote:
A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=(4/3)pie r^3 .)

(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680

Since the radius of the satellite is 4 feet, the diameter is 8 feet. So the minimum inside dimensions of the crate need to be 8 by 8 by 8.

Since the inside dimensions of the crate are consecutive even integers, the smallest such crate that can be used would have the dimension 8 by 10 by 12.

The volume of such a crate would be 8*10*12 = 960 cubic feet

I have no clue what was just discussed?VeritasPrepKarishma.. what is the Question please? any diagrams?
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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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08 Mar 2017, 00:20
deependra1234 wrote:
VeritasPrepKarishma wrote:
A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=(4/3)pie r^3 .)

(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680

Since the radius of the satellite is 4 feet, the diameter is 8 feet. So the minimum inside dimensions of the crate need to be 8 by 8 by 8.

Since the inside dimensions of the crate are consecutive even integers, the smallest such crate that can be used would have the dimension 8 by 10 by 12.

The volume of such a crate would be 8*10*12 = 960 cubic feet

I have no clue what was just discussed?VeritasPrepKarishma.. what is the Question please? any diagrams?

You have a sphere (satellite) which you have to fit into into a rectangular box (crate).
For the sphere to fit into the box, the diameter of the sphere should be less than or equal to the length, breadth and height of the box.
Hope it all makes sense now.
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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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08 Mar 2017, 00:33
since the radius is 4 ft. the smallest side should be equal to the diameter. hence the shortest side will be 8ft and therefore the rest of the side will be 10ft and 12 ft.

volume will be 8 x 10 x 12 = 960 ft^3

Option D
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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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08 Mar 2017, 02:19
radius of sphere = 4ft, so diameter is 8 ft
minimum dimension of the rectangular box will have to be 8 * 8 * 8 in order for the sphere to be perfectly fitted into the box , but the dimensions have to be consecutive integers
so the min value is 8, 10 and 12
volume of the rectangular box = 8 * 10 * 12 = 960
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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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08 Mar 2017, 04:05
Goddd and i was solving something completely different and thinking how is it a sub 600 Qs... As usual ..thankyou so much VeritasPrepKarishma
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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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12 Mar 2017, 00:36
VeritasPrepKarishma wrote:
A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=(4/3)pie r^3 .)

(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680

Since the radius of the satellite is 4 feet, the diameter is 8 feet. So the minimum inside dimensions of the crate need to be 8 by 8 by 8.

Since the inside dimensions of the crate are consecutive even integers, the smallest such crate that can be used would have the dimension 8 by 10 by 12.

The volume of such a crate would be 8*10*12 = 960 cubic feet

This is a logical and succinct explanation- thank you
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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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12 Sep 2018, 17:39
1
A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=(4/3)pie r^3 .)

(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680

The shortest dimension of the rectangular crate has to be at least the diameter of the spherical satellite; therefore, that dimension has to be at least 8. Since the dimensions of the crate are consecutive even integers, the smallest possible volume of the crate is:

8 x 10 x 12 = 960

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Re: A perfectly spherical satellite with a radius of 4 feet is being packe  [#permalink]

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03 Feb 2019, 15:41
Seems like they try to mislead you by giving you the volume for the sphere at the end. If you sketch a picture you can quickly see that it's not about the volume, but rather the 2r length of the sphere (8) which is the minimum side length. Since the sides are consecutive ints: 8*10*12 = 960, D.
Re: A perfectly spherical satellite with a radius of 4 feet is being packe   [#permalink] 03 Feb 2019, 15:41
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