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  • Volumes of two spheres are in the ratio 64 27 The ratio of their surface areas is A 3 4

Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is

(A) 3 : 4                      (B) 4 : 3                       (C) 9 : 16                     (D) 16 : 9

Answers (1)

Answer (D) 16 : 9

Let two sphere having radius r_{1} and r_{2}

According to question

\frac{\text {volume of first sphere}}{\text {volume of second sphere}}=\frac{64}{27}

\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}=\frac{64}{27}

\left ( \frac{r_{1}}{r_{2}} \right )^{3}=\frac{64}{27}

\frac{r_{1}}{r_{2}} =\sqrt[3]{\frac{64}{27}}=\frac{4}{3}

Ratio of their surface area is =\frac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}

=\frac{r_{1}^{2}}{r_{2}^{2}}=\left ( \frac{r_{1}}{r_{2}} \right )^{2}

=\left ( \frac{4}{3} \right )^{2}=\frac{16}{9}

Hence required ratio is 16 : 9

Posted by

infoexpert23

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