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

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

Answer 2

Answer:

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

Explanation:

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

$V=\dfrac{4}{3}\pi r^3$

When, r = 2 cm

$V_1=\dfrac{4}{3}\pi (2)^3$

When, r = 6 cm

$V_2=\dfrac{4}{3}\pi (6)^3$

$\dfrac{V_2}{V_1}=\dfrac{\dfrac{4}{3}\pi (6)^3}{\dfrac{4}{3}\pi (2)^3}$

$\dfrac{V_2}{V_1}=27$

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