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If p varies inversely as the cube of q and q va... - JAMB Mathematics 2006 Question

If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?
A
p varies directly as r3
B
p varies inversely as r6
C
p varies inversely as 6√P
D
p varies directly as r6
correct option: c

P ∝ 1/q3

P = K/q3

q3 = K/P

q = K/p1/3

But q ∝ r2

q = Kr2
K/p1/3 = Kr2

r2 = K/p1/3 x 1/K

r2 = 1/p1/3

r = (1/p1/3)2

r = 1/p1/6

r ∝ 1/p1/6

∴ r varies inversely as 6√P

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