Ratio of surface area

Expert replies

Cheese12: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Nov 24, 2010 12:57 am; Thanked: 3 times

by Cheese12 » Sun Oct 23, 2011 11:39 pm

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

OA:D

Hi guys,

I tried to do the question this way.. im not sure where i am going wrong. Please help to correct me.

Surface area of the Cube :
side "s" = 1 ....therefore surface area = 6

Surface area of the Rectagular object:
w= 1
l=2 (double of s)
Surface area = 2 * 6 = 12

Ratio = 6/12 = 1/2 ....

Not sure where I am going wrong

Source: Beat The GMAT — Problem Solving | Sun Oct 23, 2011 11:39 pm

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Oct 24, 2011 3:10 am

Let the sides of the cube be 1 unit. Then the surface are of the cube say SA1 = 6*(side)*(side) = 6*1*1

Then the sides of the cuboid are 1,2,1(As the length has been doubled).
Surface area of cuboid Say SA2 = 2((l*b)+(b*w)+(w*l), where l,b,w are length, breadth and width respectively.
SA2 = 2((2*1)+(1*1)+(1*2)= 2(2+1+2) = 10

Ratio = SA1/SA2 = [spoiler]6/10 = 3/5 Option D[/spoiler]

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Oct 24, 2011 3:17 am

Cheese12 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

OA:D

Hi guys,

I tried to do the question this way.. im not sure where i am going wrong. Please help to correct me.

Surface area of the Cube :
side "s" = 1 ....therefore surface area = 6

Surface area of the Rectagular object:
w= 1
l=2 (double of s)
Surface area = 2 * 6 = 12

Ratio = 6/12 = 1/2 ....

Not sure where I am going wrong

Surface area = the sums of the areas of all the faces.
In a cube, the area of each face = e², and there are 6 faces:
SA = 6e².
In a rectangular solid, the areas of the faces are lw, lh, and wh, and there are two of each type:
SA = 2(lw+lh+wh).

In the problem above:
Let e=1.
SA of the cube = 6(1²) = 6.

In the rectangular solid, since the length is doubled, l=2, w=1, and h=1.
SA = 2(2*1 + 2*1 + 1*1) = 10.

Cube/Solid = 6/10 = 3/5.

The correct answer is D.

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