Respuesta :
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:
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 :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
When, r = 2 cm
[tex]V_1=\dfrac{4}{3}\pi (2)^3[/tex]
When, r = 6 cm
[tex]V_2=\dfrac{4}{3}\pi (6)^3[/tex]
[tex]\dfrac{V_2}{V_1}=\dfrac{\dfrac{4}{3}\pi (6)^3}{\dfrac{4}{3}\pi (2)^3}[/tex]
[tex]\dfrac{V_2}{V_1}=27[/tex]
Therefore, the volume of the sphere increases by a factor of 27. Hence, this is the required solution.
