Bunuel wrote:
The stiffness of a diving board is proportional to the cube of its thickness and inversely proportional to the cube of its length. If diving board A is twice as long as diving board B and has 8 times the stiffness of diving board B, what is the ratio of the thickness of diving board A to that of diving board B? (Assume that the diving boards are equal in all respects other than thickness and length.)
A. 2
B. 4
C. 8
D. 16
E. 64
Let stiffness, thickness and length of Board A be S1, T1, and L1, and those of Board B be S2, T2, and L2
It's given S = k*T^3/L^3 - (1) (k is some constant which we don't need to worry about)
Now, since we have the relationship between S1 and S2 (Board A has 8 times the stiffness of diving board B) and L1 and L2 (Board A is twice as long as diving Board B)
Putting all these values in eq (1), we get S1/S2 = (k*T1^3/L1^3)/(k*T2^3/L2^3)
Simplifying this, we get 8 = (T1^3/T2^3)/8
Simplifying further, we get 64 = (T1/T2)^3, and solving this, we get
T1/T2 = 4, so answer choice (B) is correct
Simple solution
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