If the ratio between the radii of the two sphere is 3: 5, what is the ratio of their volumes?

a. 3: 25
b. 6: 25
c. 9: 25
d. 27: 125

Option D

Step-by-step explanation:

You know that the ratio between the radii of the two sphere is 3:5. Knowing this fact, you can calculate the ratio of their volume with this procedure:

You need to remember that:

 Then, you can rewrite it as:

Finally, you get the the ratio of the volumes of the spheres is:

or 27:125

This matches with the option D.

The ratio of their volumes is 27 : 125

Step-by-step explanation:

Points to remember

Volume of sphere V = 4/3(πr³)

Where r is the radius of sphere

To find the ratio of volume of spheres

It is given that,  the ratio between the radii of the two sphere is 3:5

V₁ =  4/3(πr₁³)  =  4/3(π3³) and

V₂ =  4/3(πr₂³) =  4/3(π5³)

V₁/V₂ = 4/3(π3³)/4/3(π5³)

 = 3³/5³ = 27/125

Therefore  the ratio of their volumes = 27 : 125