Geometry MGMAT Question Bank Q24

[abramson]

Q24 on MGMAT Q-Bank, called "Surface Comparison" is as follows:

Cylinder A, which has a radius of x and a height of y, has a greater surface area than does Cylinder B, which has a radius of y and a height of x. How much greater is the surface area of Cylinder A than that of Cylinder of B?

This problem assumes that the 2 cylinders being compared are solid cylinders and not hollow cylinders (in which case we would not add the surface area for the top and bottom). Is this a standard assumption we could make for all GMAT cylinder problems?

Thanks for any comments.

[Harish Dorai]

You are right! Unless it is explicitly mentioned we should assume that the cylinder has 2 circular faces. Also on your point on hollow cylinders - A cylinder can be hollow and still have 2 circular faces Ex: Any empty coke can ;-) It all depends on what object is visualized as a cylinder. Some examples of the common visualizations for cylinder I have seen is:

1) An empty cylindrical drum with a face open. This is a cylinder with one circular base and hence we should consider only one circle in calculating the area.

2) A cylindrical pipe which has got a certain thickness. This can be considered as a hollow cylinder which will have concentric circular base (You should calculate the circular base area by subtracting the area of inner circle from outer circle).

Hope it helps!

[unique]

So in this case SA = pi*x^2*y + 2 * pi* x^2
and SB = pi * y^2*x + 2 *pi * y^2

and then Sa - Sb - is that correct?

I did not think of it as a solid cyclinder till I read ur explaination!!!

[abramson]

thanks so much!

[StaceyKoprince]

to address part of the original poster's question - yes, you assume on the test that a given shape is solid (all relevant surfaces) unless they tell you otherwise. A cylinder, a pyramid, a sphere - whatever.