Questions involving rectangular solids, particularly data sufficiency questions, test whether you understand the concept of volume and surface area. You essentially need to remember that you need three different values to find volume and surface area (the length, the width and the height). If the prompt and statements 1 and 2 are lacking some these values or some way to find them, neither of the statements will be sufficient.
Try this GMAT volume question for more practice.
A rectangular solid is formed by 3 pairs of similar rectangular faces. In other words, 6 rectangular faces in total.
The formulas you need to remember for a rectangular solid are
Volume = Length (l) x Width (w) x Height (h)
Surface Area = (2 x Length x Width) + (2 x Length x Height) + (2 x Width x Height)
If length = width = height, that means that the rectangular solid is, in fact, a cube.
Other vocabulary that might be important is the terms vertex and edge. A vertex is a mathematical way of referring to the corner of any figure. The rectangular solid above has 8 vertices (plural of vertex), can you identify them? The edge is simply the lines you see in the diagram above: the line where two surfaces meet.
Questions involving cylinders are similar and perhaps easier because there are only two values you need to know to solve cylinder-problems – the radius (r) and the height (h).
If you don’t know the radius, anything that enables you to determine the radius, such as the diameter (radius = diameter / 2) or the circumference (radius = circumference / 2pi) will suffice.
Regarding cylinders, the formulas you need to know are
Volume = area of the base circle x height = pi x (radius)2 x height
Surface Area = (2 x pi x (radius)2 )+ (pi x (diameter) x height)
Let’s try a problem: A cylindrical water tank has a stripe painted around its circumference, as shown in the figure provided. What is the surface area of this stripe?
(1) y = 0.7
(2) The height of the tank is 2 meters.
To find the surface area of the stripe, you need to know the circumference of the cylinder, but there is not data in the question that gives you the radius or diameter to let you find the circumference. Hence the answer should be that neither statement together is sufficient.
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