Question

If the radius of a sphere is reduced to one-third, by how many times does its
volume decrease?​

Answer 1

Given :

• The radius of a sphere is reduced to one-third.

To find :

• Its Volume decrease =?

Formula Used :

• Volume of sphere = 4/3 π r³

Step-by-step explanation :

It is Given that :

The radius of a sphere is reduced to one-third,

So, Radius = r × 1/3 = r/3

Now,

As We know that :

Volume of sphere = 4/3 π r³

Substituting the values in the above formula, we get,

= 4/3 × π × (r/3)³

= 4/3 × π × r³/27.

Therefore, We can say that new Volume 1/27 times decreased.

Answer 2

Given :

• Radius of the sphere is reduced to one-third.

To find :

• Its volume decreased

Explanation :

Since the radius of the sphere is reduced to one-third,

•°• Radius = r × 1/3 = r/3

Now, as we know that,

Volume of sphere = 4/3 πr³

Substituting the values in the above formula, we get,

=> 4/3 × π × (r/3)³

=> 4/3 × π × r³/27

Hence, we can say that the new volume decreases by 1/27 times.