What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
1/4
3/8
1/2
3/5
2
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neelgandham
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Let side of the cube = a, then Length of the rectangular solid is 2a, width a and breadth a.
Surface area of cube = 6*a^2
Surface area of the rectangular solid = 2(a*2a + 2a*a + a*a) = 10*a^2
Ratio of the surface area of a cube to the surface area of a rectangular solid = 6*a^2/(10*a^2) = 3/5
Note:
Surface area of cube =6 * square of a side.
Surface area of a cuboid = 2((Length * Breadth) + (Breadth * Width) + (Width * Length))
Surface area of cube = 6*a^2
Surface area of the rectangular solid = 2(a*2a + 2a*a + a*a) = 10*a^2
Ratio of the surface area of a cube to the surface area of a rectangular solid = 6*a^2/(10*a^2) = 3/5
Note:
Surface area of cube =6 * square of a side.
Surface area of a cuboid = 2((Length * Breadth) + (Breadth * Width) + (Width * Length))
Anil Gandham
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Anurag@Gurome
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Let us assume that side of cube = sGmatKiss wrote:What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
1/4
3/8
1/2
3/5
2
Then length of rectangular solid = 2s, width = height = s
Now surface area of a cube = 6 * (side)² = 6s²
and surface area of rectangular solid = 2(length * width + length * height + width * height) = 2(2s² + 2s² + s²) = 2(5s²) = 10s²
So, required ratio = 6s² : 10s² = [spoiler]3 : 5[/spoiler]
The correct answer is D.
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GMATGuruNY
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The surface area of a cube = 6e².GmatKiss wrote:What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
1/4
3/8
1/2
3/5
2
The surface area of a rectangular solid = 2(lw + lh + wh).
Let the edge of the cube = 1.
Thus, the surface area = 6(1²) = 6.
In the rectangular solid, since the length is doubled, l=2, w=1 and h=1.
Thus, the surface area = 2(2*1 + 2*1 + 1*1) = 10.
Cube/Solid = 6:10 = 3:5.
The correct answer is D.
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