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Firlakuza [10]
4 years ago
8

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

Mathematics
2 answers:
atroni [7]4 years ago
5 0
The ratio of theire volumes is 5^3 : 8^3
which is  125: 512
oee [108]4 years ago
5 0

Answer:  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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2 years ago
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<em>Comment on fractions and parentheses</em>

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