Answer:
Relation between V and c is represented as:
[tex]V = \pi c^{3}[/tex]
When c is halved, V becomes [tex]\frac{1}{8}[/tex] of its initial value.
Step-by-step explanation:
Height of cylinder = Radius of cylinder = c
Volume of cylinder = V
As per formula:
[tex]V = \pi r^{2} h[/tex]
Where [tex]r[/tex] is the radius of cylinder and
[tex]h[/tex] is the height of cylinder
Putting [tex]r = h =c[/tex]
[tex]V = \pi c^{2} \times c\\\Rightarrow V = \pi c^{3} ......(1)[/tex]
The values of c is halved:
Using equation (1), New volume:
[tex]V' = \pi (\dfrac{c}{2})^3\\\Rightarrow \dfrac{1}{8} \pi c^{3}[/tex]
By equation (1), putting [tex]\pi \times c^{3} = V[/tex]
[tex]V' = \dfrac{1}{8} \times V[/tex]
So, when c is halved, V becomes [tex]\frac{1}{8}[/tex] of its initial value.
