A perfume industry currently packages its products in spherical bottles with radius $R$, with volume given by $\frac{4}{3}\pi \cdot (R)^{3}$. It was observed that there will be a cost reduction if cylindrical bottles are used with base radius $\frac{R}{3}$, whose volume will be given by $\pi\left(\frac{R}{3}\right)^{2} \cdot h$, where $h$ is the height of the new packaging. For the same capacity of the spherical bottle to be maintained, the height of the cylindrical bottle (in terms of $R$) should be equal to (A) $2R$. (B) $4R$. (C) $6R$. (D) $9R$. (E) $12R$.
A perfume industry currently packages its products in spherical bottles with radius $R$, with volume given by $\frac{4}{3}\pi \cdot (R)^{3}$.
It was observed that there will be a cost reduction if cylindrical bottles are used with base radius $\frac{R}{3}$, whose volume will be given by $\pi\left(\frac{R}{3}\right)^{2} \cdot h$, where $h$ is the height of the new packaging.
For the same capacity of the spherical bottle to be maintained, the height of the cylindrical bottle (in terms of $R$) should be equal to
(A) $2R$.
(B) $4R$.
(C) $6R$.
(D) $9R$.
(E) $12R$.