Question

There are many cylinders for which the height and radius are the same value. Let

Answer 1

Answer:

Relation between V and c is represented as:

$V = \pi c^{3}$

When c is halved, V becomes $\frac{1}{8}$ of its initial value.

Step-by-step explanation:

Height of cylinder = Radius of cylinder = c

Volume of cylinder = V

As per formula:

$V = \pi r^{2} h$

Where $r$ is the radius of cylinder and

$h$ is the height of cylinder

Putting $r = h =c$

$V = \pi c^{2} \times c\\\Rightarrow V = \pi c^{3} ......(1)$

The values of c is halved:

Using equation (1), New volume:

$V' = \pi (\dfrac{c}{2})^3\\\Rightarrow \dfrac{1}{8} \pi c^{3}$

By equation (1), putting $\pi \times c^{3} = V$

$V' = \dfrac{1}{8} \times V$

So, when c is halved, V becomes $\frac{1}{8}$ of its initial value.