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The cube has edges of length 10.
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21 Dec 2022, 11:48
21 Dec 2022, 11:48
Expert Reply
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Question Stats:
68% (00:57) correct
32% (01:13) wrong based on 25 sessions
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GRE The cube has edges of length 10..jpg [ 28.73 KiB | Viewed 1705 times ]
The cube has edges of length 10.
Quantity A |
Quantity B |
The length of the diagonal from point A to point B |
17 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
The cube has edges of length 10.
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03 Feb 2024, 20:37
03 Feb 2024, 20:37
2
The diagonal of a solid cube is given by the formula \(a \sqrt{3}\)
Since \(a=10\), the diagonal stretching from A to B will be \(10 \sqrt{3} = 10 \times 1.732 = 17.32\)
Quantity A = 17.32
Quantity B = 17
Quantity A is the greatest.
Derivation of the length of Diagonal is as follows
Draw a line AC as show below. Let \(a\) be the length of the edge of the cube. In this problem \(a=10\)
GRE The cube has edges of length 10..jpg [ 23.26 KiB | Viewed 855 times ]
Now \(AC^2 = a^2 + a^2\)
\(AC^2 = 2a^2\)
\(AC = a \sqrt{2}\)
Now ABC is a right angled triangle where AB is the hypotenuse. Length of AB is given by
\(AB^2 = AC^2 + BC^2\)
\(AB^2 = (a \sqrt{2})^2 + a^2\)
\(AB^2 = 2a^2 + a^2\)
\(AB^2 = 3a^2\)
\(AB = a \sqrt{3}\)
This is the result we used to solve the problem
Since \(a=10\), the diagonal stretching from A to B will be \(10 \sqrt{3} = 10 \times 1.732 = 17.32\)
Quantity A = 17.32
Quantity B = 17
Quantity A is the greatest.
Derivation of the length of Diagonal is as follows
Draw a line AC as show below. Let \(a\) be the length of the edge of the cube. In this problem \(a=10\)
Attachment:
GRE The cube has edges of length 10..jpg [ 23.26 KiB | Viewed 855 times ]
Now \(AC^2 = a^2 + a^2\)
\(AC^2 = 2a^2\)
\(AC = a \sqrt{2}\)
Now ABC is a right angled triangle where AB is the hypotenuse. Length of AB is given by
\(AB^2 = AC^2 + BC^2\)
\(AB^2 = (a \sqrt{2})^2 + a^2\)
\(AB^2 = 2a^2 + a^2\)
\(AB^2 = 3a^2\)
\(AB = a \sqrt{3}\)
This is the result we used to solve the problem
General Discussion
The cube has edges of length 10.
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04 Jan 2023, 03:02
04 Jan 2023, 03:02
Expert Reply
You can solve this using the formula \(d^2=l^2+w^2+h^2\) and mover from here.
This is not a so hard question and it is quite useful to stretch your mental muscles and try to figure out alternative ways to solve it. As such, you can training yourself to see shortcuts or different ways to solve hardest questions ahead
GRE The cube has edges of length 10..jpg [ 29.09 KiB | Viewed 1649 times ]
If you draw a diagonal as in the figure, you will recognize that we do have an isosceles triangle in which two sides are equal and one not
In this specific triangle, we do have also the trifecta
\(x:x:x \sqrt{3}\)
because the two sides are = 10 the third is \(x \sqrt{3}\)
\(10 \sqrt{3 }> 17\)
A is the answer
screenshot.1166.jpg [ 51.84 KiB | Viewed 1582 times ]
This is not a so hard question and it is quite useful to stretch your mental muscles and try to figure out alternative ways to solve it. As such, you can training yourself to see shortcuts or different ways to solve hardest questions ahead
Attachment:
GRE The cube has edges of length 10..jpg [ 29.09 KiB | Viewed 1649 times ]
If you draw a diagonal as in the figure, you will recognize that we do have an isosceles triangle in which two sides are equal and one not
In this specific triangle, we do have also the trifecta
\(x:x:x \sqrt{3}\)
because the two sides are = 10 the third is \(x \sqrt{3}\)
\(10 \sqrt{3 }> 17\)
A is the answer
Attachment:
screenshot.1166.jpg [ 51.84 KiB | Viewed 1582 times ]
