The volumes of the two spheres are in the ratio 64:27. Find the ratio of their surface areas.

 

Answers (1)

Answer : 16:9

We have been given that the volume of two sphere is in the ratio =64:27

We know that, Volume of sphere is given as \frac{4}{3}\pi r^{3} (where r is its radius)

And surface area is given as 4\pi r^{2}

Let volume of sphere 1=V_{1}         (radius r_{1})

And, volume of sphere 2=V_{2}        (radius r_{2})

Then, \frac{V_{1}}{V_{2}}=\frac{64}{27}

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

\frac{r_{1}^{3}}{r_{2}^{3}}=\left ( \frac{4}{3} \right )^{3}

\frac{r_{1}}{r_{2}}=\frac{4}{3}

Then, ratio of areas of both spheres

\frac{\text {area of sphere (1))}}{\text {area of sphere }(2)}=\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 the required ratio is 16:9

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