What is the ratio of the surface area of a cube to the surfa

why "4+4+2" if there are two cubes than it should be "4+4" = 8 faces

Plus 2 faces on the top and bottom. Put two dice one on another and see how many faces will it have.

Area of cube = \(a^2 + a^2 + a^2 + a^2 + a^2 + a^2 = 6 a^2\)

When one of the dimension is doubled, it has impact on 4 sides (rest 2 remains same)

Look at the diagram

Area of rectangular solid \(= a^2 + a^2 + 2 a^2 + 2 a^2 + 2 a^2 + 2 a^2 = 10 a^2\)

Ratio \(= \frac{6 a^2}{10 a^2} = \frac{3}{5}\)

Answer = D

Another way to think about it:

Imagine the cube with 6 equal faces. The surface area will be 6s^2 (s is the length of the edge of the cube).
Now imagine pulling on one face of the cube to elongate it. Now you have 4 extra equal faces on the four sides. The extra surface area is 4s^2.

Ratio of surface area of cube:surface area of rectangular solid = 6:10 = 3:5

Answer (D)

Hi All,

This question can be solved by TESTing VALUES. You would likely find it helpful to physically draw the cube and solid.

Since the answer choices do not include variables, we can use whatever values we'd like for the dimensions of the cube and for the rectangular solid (as long as we follow the Facts described in the prompt). Given the one specific rule (the length of the rectangular solid is double the length of the cube), I'll TEST the easiest VALUES that I can think of...

Cube = (1)(1)(1)
Solid = (1)(1)(2)

Surface Area of Cube = 6(1) = 6
Surface Area of Solid = 2(1) + 4(2) = 10

Thus, the ratio of the two Surface Areas is 6:10 = 3:5

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Could someone help me understand the fault in my logic?

1: Assume the measurements of the cube is 2 ft x 2 ft x 2 ft.
- Area runs out to be 8 ft^3

2: Apply restrictions to rectangular solid so measurements are 4 ft x 2 ft x 2 ft
- Area runs out to be 16 ft^3

3: Assess ratio of cube to rectangle
- 8 / 16 = 1/2

Hi lmcclellan18,

Your example fits perfectly, but you calculated the VOLUMES of the two shapes - and the prompt asks us to compare the SURFACE AREAS of the two shapes. Using your example, if you calculate those two total surface areas, then you'll end up with the correct answer.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com

Hi - The question doesn't explicitly mention to find the ratio of total surface area of the asked figures. How do we know if we should calculate the ratio of TSA (Total Surface Area) or CSA(Curved Surface Area) of these solid figures? Question looks ambigous.

Hi Traj201090,

'Curved Surface Area' is really only an issue for solids that have 'curves' in them (such as spheres, cylinders, cones, etc.). In this prompt, we're dealing with a CUBE and a 2nd Rectangular Solid - and neither of those shapes have curves. Even if you did not make that distinction though, when you calculate the total surface area of each of the two shapes - and compare those surface areas as a ratio - you'll only end up with one answer.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com

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