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30 Aug 2024, 04:44
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1 x 6 row: 28%
2 x 3 matrix: 39%
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
58% (03:15) correct
42%
(03:24)
wrong
based on 949
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Six identical solid metal cubes are to be polished with gold on all surfaces before being displayed in a showroom. To reduce the amount of gold needed for polishing, the showroom managers are contemplating welding the six cubes together, thereby forming a rectangular solid before polishing. They are contemplating two ways of doing so - by joining all six cubes together (1 × 6 row) and forming a long, rectangular solid or by forming a 2 × 3 matrix.
In the table, select the values that, approximately, represent the percentage of gold saved in polishing the solids by joining them in 1 × 6 row and 2 × 3 matrix respectively, compared to the amount of gold needed if the six cubes were to be polished separately. Make only two selections, one in each column.
In the table, select the values that, approximately, represent the percentage of gold saved in polishing the solids by joining them in 1 × 6 row and 2 × 3 matrix respectively, compared to the amount of gold needed if the six cubes were to be polished separately. Make only two selections, one in each column.
| 1 x 6 row | 2 x 3 matrix | Percentage saving |
| 20% | ||
| 28% | ||
| 33% | ||
| 39% | ||
| 42% |
ShowHide Answer
Official Answer
1 x 6 row: 28%
2 x 3 matrix: 39%
30 Aug 2024, 09:34
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Let's assume that the side of the cube is of length = x
In the base case,
Surface area of a cube = 6x^2
Surface area of 6 cubes = 6* 6x^2 = 36x^2
Case 1:
1x6 Matrix
This is a cuboid of length = 6x, breadth =x, and height = x.
Surface area = 2 * x^2 + 4 * (6x*x) = 2x^2 + 24x^2
= 26x^2
Savings in area over base case = (36x^2 - 26x^2 )/36x^2 = 10/36 = 28%
Case 2:
2x3 Matrix
This is a cuboid of length =3x, breadth = 2x and height = 2x
Surface area = 2 * ( 2x*3x + x*2x + x*3x)
= 22x^2
Savings in area over base case = (36x^2 - 22x^2)/36^2 = 14/36 = 39%
In the base case,
Surface area of a cube = 6x^2
Surface area of 6 cubes = 6* 6x^2 = 36x^2
Case 1:
1x6 Matrix
This is a cuboid of length = 6x, breadth =x, and height = x.
Surface area = 2 * x^2 + 4 * (6x*x) = 2x^2 + 24x^2
= 26x^2
Savings in area over base case = (36x^2 - 26x^2 )/36x^2 = 10/36 = 28%
Case 2:
2x3 Matrix
This is a cuboid of length =3x, breadth = 2x and height = 2x
Surface area = 2 * ( 2x*3x + x*2x + x*3x)
= 22x^2
Savings in area over base case = (36x^2 - 22x^2)/36^2 = 14/36 = 39%
