Question

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

Answer 1

Answer: 125:512

Explanation:

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Answer 2

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=(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

`(V)/(V')=((4)/(3)\pi r^3)/((4)/(3)\pi R^3)=(r^3)/(R^3)=\left((r)/(R)\right)^3=\left((5)/(8)\right)^3=(125)/(512)\\\\\\\Rightarrow V:V'=125:512.`

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