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A cube has a volume of 125 cubic centimeters. What is the length, in

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Bunuel
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A cube has a volume of 125 cubic centimeters. What is the length, in [#permalink] New post   21 Aug 2018, 20:58
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A cube has a volume of 125 cubic centimeters. What is the length, in centimeters, of the longest possible straight line distance between two corners of the cube?

A. 5√2
B. 5√3
C. 10
D. 10√2
E. 20
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B
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Re: A cube has a volume of 125 cubic centimeters. What is the length, in [#permalink] New post   21 Aug 2018, 21:05
Bunuel wrote:
A cube has a volume of 125 cubic centimeters. What is the length, in centimeters, of the longest possible straight line distance between two corners of the cube?

A. 5√2
B. 5√3
C. 10
D. 10√2
E. 20


Given, volume of cube=125cc
So, side length of the cube=5 cm

The longest possible straight line distance between two corners of the cube=\(\sqrt{3}\)*measure of side of the cube=\(\sqrt{3}*5=5√3\)

Ans. (B)
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Re: A cube has a volume of 125 cubic centimeters. What is the length, in [#permalink] New post   21 Aug 2018, 21:09
Volume of cube = S^3 = 125
S = 5

The longest possible straight line distance between two corners of the cube is nothing but diagonal of the cube.

As it is a Cube, l=b=h

Diagonal of cube = √l^2+b^2+h^2
= √25+25+25
= √75
= 5√3

Hence B

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Re: A cube has a volume of 125 cubic centimeters. What is the length, in [#permalink] New post   21 Aug 2018, 22:04
Bunuel wrote:
A cube has a volume of 125 cubic centimeters. What is the length, in centimeters, of the longest possible straight line distance between two corners of the cube?

A. 5√2
B. 5√3
C. 10
D. 10√2
E. 20

Each side of the cube = 5 cm

Diagonal of the cube is = 5√3 (Answer must be B)
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Re: A cube has a volume of 125 cubic centimeters. What is the length, in [#permalink] New post   22 Aug 2018, 00:57
Ans B
5sqrt3

The larger line will be from the bottom corner to the top corner in diagonal plane.

The bottom line will be a diagonal of the bottom square= 5sqrt2
The height = 5
Diagonal from bottom to top corner in different plane = sqrt of the sun of squares of the above two = 5sqrt3



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Re: A cube has a volume of 125 cubic centimeters. What is the length, in [#permalink]
22 Aug 2018, 00:57
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