Question

24. If the ratio of volumes of two spheres is 1 : 8,
then the ratio of their surface areas is
(A) 1:2
(8) 1:4
(0) 1:6
(D) 1:8​

Answer 1

Answer:

I hope this helps you!!

Answer 2

The ratio of the two surface areas is 1 : 4.

Step-by-step explanation:

The volume of a sphere is:

$V=\frac{4}{3}\pi r^{3}$

The ratio of the volumes of two spheres is 1 : 8.

Compute the ratio of the radii as follows:

    $\frac{V_{1}}{V_{2}}=\frac{1}{8}$

$\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}=\frac{1}{8}$

$(\frac{r_{1}}{r_{2}})^{3}=(\frac{1}{2})^{3}$

    $\frac{r_{1}}{r_{2}}=\frac{1}{2}$

The surface area of a sphere is:

$SA=4\pi r^{2}$

Compute the ratio of the two surface areas as follows:

$\frac{SA_{1}}{SA_{2}}=\frac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}$

      $=(\frac{r_{1}}{r_{2}})^{2}$

      $=(\frac{1}{2})^{2}$

      $=\frac{1}{4}$

Thus, the ratio of the two surface areas is 1 : 4.

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