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

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

by Vincen » Fri Jan 28, 2022 5:10 am

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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) $$2\sqrt[3]{36}$$