What is the length of an edge of a cube whose total surface area is X cm\(^2\) and whose volume is \(\frac{X}{2}\)cm\(^3\)?
A
3
B
6
C
9
D
12
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Total surface area of cube = 6s\(^2\)
6s\(^2\) = x
s\(^2\) = x = \(\frac{x}{6}\).....(1)
volume of a cube = s\(^2\) = \(\frac{x}{2}\)
s\(^2\) = \(\frac{x}{2}\)......(2)
put(1) into (2)
s(\(\frac{x}{6}\)) = \(\frac{x}{2}\)
s = \(\frac{x}{2} \times \frac{6}{x}\)
= 3cm
Source: Myschool Past Questions Archive (Record #36383)