Question

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

Answer 1

The ratio of their volumes is 27 : 125

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

Answer 2

Answer: Option D

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:

`ratio\ volume=(3^3)/(5^3)`

You need to remember that:

`a^3=a*a*a`

Then, you can rewrite it as:

`ratio\ volume=(3*3*3)/(5*5*5)`

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

`ratio\ volume=(27)/(125)` or 27:125

This matches with the option D.