If x varies inversely as the cube root of y and x = 1 when y = 8, find y when x = 3

A.
(frac{1}{3}) 
B.
(frac{2}{3}) 
C.
(frac{8}{27}) 
D.
(frac{4}{9})
Correct Answer: Option C
Explanation
(x propto frac{1}{sqrt[3]{y}} implies x = frac{k}{sqrt[3]{y}})
When y = 8, x = 1
(1 = frac{k}{sqrt[3]{8}} implies 1 = frac{k}{2})
(k = 2)
(therefore x = frac{2}{sqrt[3]{y}})
When x = 3,
(3 = frac{2}{sqrt[3]{y}} implies sqrt[3]{y} = frac{2}{3})
(y = (frac{2}{3})^{3} = frac{8}{27})