Question

The volume of a sphere increases with the cube of its radius. If the radius of a sphere increases from 2cm to 6cm, by what factor does is volume increase?

Answer 1

The volume of the sphere increases by a factor of 27.

Step-by-step explanation:

We know that, the volume of a sphere increases with the cube of its radius. Mathematically, it is given by :

`V=(4)/(3)\pi r^3`

When, r = 2 cm

`V_1=(4)/(3)\pi (2)^3`

When, r = 6 cm

`V_2=(4)/(3)\pi (6)^3`

`(V_2)/(V_1)=((4)/(3)\pi (6)^3)/((4)/(3)\pi (2)^3)`

`(V_2)/(V_1)=27`

Therefore, the volume of the sphere increases by a factor of 27. Hence, this is the required solution.

Answer 2

Answer;

volume increases with a factor of 27

Explanation;

The volume of a sphere is given by the formula

V = 4/3 πr³

When the radius is 2 cm the volume will be;

V = 4/3 π (2)³

= 32/3 π

When the increases to 6 cm the volume will be ;

V = 4/3 π (6)³

= 864/3 π

Hence, the volume increases by a factor;

(864/3 π) ÷ (32/3 π)

= 27

Thus, the volume increases with a factor 27