For a party, three solid cheese balls with diameters of \(2\) inches, \(4\) inches, and \(6\) inches, respectively, were

For a party, three solid cheese balls with diameters of \(2\) inches, \(4\) inches, and \(6\) inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is \(\dfrac43\pi r^3,\) where \(r\) is the radius.)

(A) \(12\)

(B) \(16\)

(C) \(\sqrt[3]{16}\)

(D) \(3\sqrt[8]8\)

(E) \(2\sqrt[3]{36}\)

Answer: E

Source: Official Guide