Respuesta :
If im not wrong
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
The volume of the sphere is calculated by the formula [tex]\dfrac{4}{3}\pi r^3[/tex], where r is radius of the sphere.
Given that, the radius of the sphere increased from 2 cm to 6 cm, such that:
V = [tex]\dfrac{4}{3}\pi r^3[/tex]
where, radius = 2 cm
V = [tex]\dfrac{4}{3}\pi \;(2)^3[/tex]
V = [tex]\dfrac{32}{3}\pi[/tex]
Now, when the radius increased from 2 cm to 6 cm, such that:
[tex]\rm V = \dfrac{4}{3}\pi r^3\\\\\rm V = \dfrac{4}{3}\pi (6)^3\\\\\rm V = \dfrac{864}{3}\pi[/tex]
Now, the volume will increase by the factor:
[tex]\rm V = \dfrac{864}{3}\pi \;\div\; \dfrac{32}{3}\pi\\\\\rm V = 27[/tex]
Thus, the volume of the sphere will increase by the factor 27.
To know more about volume, refer to the following link:
https://brainly.com/question/16924154
