Mathematics: If the ratio between the radii of the two spheres is 5: 8, what is the ratio of their volumes?

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If the ratio between the radii of the two spheres

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karatekats1

13.01.2022

Mathematics

The required ratio of the volumes of two spheres is 125 : 512.

Step-by-step explanation: Given that the ratio between the radii of the two spheres is 5 : 8.

We are to find the ratio of the volumes of the two spheres.

Let, 'r' and 'R' represents the radii of the two spheres, so

r : R = 5 : 8.

The volume of a sphere with radius 'r' units is given by the formula:

$V=\dfrac{4}{3}\pi r^3.$

Let, V and V' be the volumes of the spheres with radius r and R units respectively.

Then, the ratio of the volumes of the two spheres will be

$\dfrac{V}{V'}=\dfrac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\dfrac{r^3}{R^3}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{5}{8}\right)^3=\dfrac{125}{512}\\\\\\\Rightarrow V:V'=125:512.$

Thus, the required ratio of the volumes of two spheres is 125 : 512.

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If the ratio between the radii of the two spheres is 5: 8, what is the ratio of their volumes?

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