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The volume of the rectangular solid above is 720. If AF = 15, which of

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Carcass
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The volume of the rectangular solid above is 720. If AF = 15, which of [#permalink] New post   05 Dec 2022, 02:55
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The volume of the rectangular solid above is 720. If AF = 15, which of the following is closest to the distance from C to F ?

6
8
12
15
18
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E
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GeminiHeat
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Re: The volume of the rectangular solid above is 720. If AF = 15, which of [#permalink] New post   07 Dec 2022, 07:42
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Volume = l*w*h
720=6∗15∗X

X=8

Distance from A to E

82+152=172

Distance C to F

172+62=
289+36=325

325 is approximately 182

Answer: E
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Re: The volume of the rectangular solid above is 720. If AF = 15, which of [#permalink] New post   09 Dec 2022, 04:00
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OE


The distance from C to F is the diagonal of the box, so use the Super Pythagorean theorem: a^2 + b^2 + c^2 = d^2, where a, b, and c are the sides of the box and d is the diagonal. You have the length and height of the box, so use the volume formula to find the width: 720 = (15)(6)w, so the width is 8. Now plug your numbers into the formula: 15^2 + 8^2 + 6^2 = d^2, so 325 = d^2, and d = 18.03.
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Chanchal
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Re: The volume of the rectangular solid above is 720. If AF = 15, which of [#permalink] New post   05 Aug 2024, 09:35
Carcass wrote:
OE


The distance from C to F is the diagonal of the box, so use the Super Pythagorean theorem: a^2 + b^2 + c^2 = d^2, where a, b, and c are the sides of the box and d is the diagonal. You have the length and height of the box, so use the volume formula to find the width: 720 = (15)(6)w, so the width is 8. Now plug your numbers into the formula: 15^2 + 8^2 + 6^2 = d^2, so 325 = d^2, and d = 18.03.



Can you please explain the second PArt?
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Re: The volume of the rectangular solid above is 720. If AF = 15, which of [#permalink] New post   05 Aug 2024, 10:36
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we need to find is the longest digonal
in this case l*b*h= 720
given l = 15
so b*h = 48
b& h have to be < L
so
best option 6*8*15 =720
or say √6^2+8^2+15^2 = 18
IMO E
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Re: The volume of the rectangular solid above is 720. If AF = 15, which of [#permalink] New post   14 Oct 2024, 12:56
How do people know the length is 6? that's the only piece I don't get
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Re: The volume of the rectangular solid above is 720. If AF = 15, which of [#permalink] New post   14 Oct 2024, 13:32
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6 is mentioned in the figure above. It is the side DE
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Re: The volume of the rectangular solid above is 720. If AF = 15, which of [#permalink]
14 Oct 2024, 13:32
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