The volume is One-fourth of the original.
"It is a three dimensional structure having two parallel bases joined by a curved surface, at a fixed distance."
V = π × r² × h, where 'r' is the radius of the circular base and 'h' is the height of the cylinder.
In the given question,
the radius of the cylinder is 10 cm, and the height is 14 cm.
⇒ r = 10 cm, h = 14 cm
The volume of the cylinder would be,
[tex]V_1=\pi\times 10^2\times 14\\\\V_1=\frac{22}{7}\times 100 \times 14\\\\V_1=4400~~cu.~cm.[/tex]
If the radius is halved, the radius becomes 5 cm.
The new volume of a cylinder would be,
[tex]V_2=\pi \times 5^2\times 14\\\\V_2=\frac{22}{7}\times 25 \times 14\\\\V_2=1100~~cu.~cm.[/tex]
The ratio between the original and the new volume of the cylinder is:
[tex]\Rightarrow \frac{1100}{4400}=\frac{1}{4}\\\\\Rightarrow V_2=\frac{1}{4}V_2[/tex]
This means, the volume is One-fourth of the original.
Learn more about cylinder here:
https://brainly.com/question/24084532
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