Question

For a party , three solids 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 $\frac{4}{3}\pi r^3$ , where r is the radius.)

• A. $12$
• B. $16$
• C. $\sqrt[3]{316}$
• D. $3\sqrt[3]{38}$
• E. $2\sqrt[3]{336}$

Answer 1

The correct option is E $2\sqrt[3]{336}$

Volume of new chase ball = $\frac{4}{3}\pi (r_1^3+r_2^3+r_3^3)$

$\Rightarrow \frac{4}{3}\pi r^2=\frac{4}{3}\pi ({\left(2\right)}^3+{\left(4\right)}^3+{\left(6\right)}^3)\Rightarrow R^3=8+64+216$

$\Rightarrow R=\sqrt[3]{3288}=\sqrt{8\times 36}=2\sqrt[3]{336}$ inch