DSQ: Calculating the diagonal of a prism - GMAT Quantitative Reasoning
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Find the length of the diagonal of cube 
.
I) 
has a volume of 
.
II) 
has a surface area of 
.
Find the length of the diagonal of cube
I)
II)
To find the length of the diagonal, we need the side length.
I) Gives us the volume of the cube. Take the cubed root to find the side length.
II) Gives us the surface area, divide by 6 (the number of faces in a cube) and take the square root to find the side length.
Diagonal of a cube is the side length times the square root of three. Alternatively, this can be found using the Pythagorean Theorem twice.
Either way, we can use I) or II) to find our side lenght and then our diagonal.
To find the length of the diagonal, we need the side length.
I) Gives us the volume of the cube. Take the cubed root to find the side length.
II) Gives us the surface area, divide by 6 (the number of faces in a cube) and take the square root to find the side length.
Diagonal of a cube is the side length times the square root of three. Alternatively, this can be found using the Pythagorean Theorem twice.
Either way, we can use I) or II) to find our side lenght and then our diagonal.
Compare your answer with the correct one above
What is the diagonal of a rectangular prism?
-
Its surface area is 
-
Its height = twice its width = thrice its length.
What is the diagonal of a rectangular prism?
-
Its surface area is
-
Its height = twice its width = thrice its length.
The diagonal of a rectangular prism is found via the formula 
The second statement reduces this to 
However, the actual length is unknown. Statement 1 allows the calculation of a numerical value:
The diagonal of a rectangular prism is found via the formula
The second statement reduces this to
However, the actual length is unknown. Statement 1 allows the calculation of a numerical value:
Compare your answer with the correct one above